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At least 1,441 records · Page 80

Reduced‐Order Modeling of Energetic Materials Using Physics‐Aware Recurrent Convolutional Neural Networks in a Latent Space (LatentPARC)

Physics-aware deep learning (PADL) has gained popularity for use in spatiotemporal dynamics simulations, such as those in computational modeling of energetic materials (EM). We show that the challenge PADL methods face while learning complex field evolution problems can be simplified and accelerated by decoupling it into two tasks: learning complex geometric features in evolving fields and modeling dynamics over these features in a lower-dimensional feature space. We build upon our previous work on physics-aware recurrent convolutional neural networks (PARC). PARC embeds knowledge of underlying physics into its neural network architecture for more robust and accurate prediction of evolving physical fields. PARC was shown to effectively learn complex nonlinear features such as the formation of hotspots and coupled shock fronts in various initiation scenarios of EMs, as a function of microstructures, serving effectively as a microstructure-aware burn model. Here, we further accelerate PARC and reduce its computational cost by projecting the original dynamics onto a lower-dimensional invariant manifold, or “latent space.” The projected latent representation encodes the complex geometry of evolving fields (e.g., temperature and pressure) in a set of data-driven features. The reduced dimension of this latent space allows us to learn the dynamics during the initiation of EM with a lighter and more efficient model. We observe a significant decrease in training and inference time while maintaining results comparable to PARC at inference. This work takes steps towards enabling rapid prediction of EM thermomechanics at larger scales and characterization of EM structure–property–performance linkages at a full application scale.

Mathematics and Computing↗

On the strength and fracture toughness of an additive manufactured CrCoNi medium-entropy alloy

An additively manufactured (nominally equiatomic) CrCoNi alloy was processed by laser powder bed fusion (LPBF). At ambient temperatures (298 K), this medium-entropy alloy displayed a yield strength, σ y of ~691 ± 9 MPa, and an ultimate tensile strength, σ u of ~926 ± 15.2 MPa; at cryogenic temperatures (77 K), yield and tensile strengths increased respectively to σ y ~ 944 ± 6 MPa and σ u ~ 1382 ± 11 MPa. These strength levels are 57 and 44% higher than that of the wrought alloy, due to strengthening from the solidification cellular structures intertwined with dislocations in the LPBF CrCoNi. The crack-initiation fracture toughness, K JIc was measured to be ~183.7 ± 28 MPa√m at 298 K; this value marginally decreased by ~4% to ~176 ± 11 MPa√m at 77 K. These K JIc values of the LPBF CrCoNi were 11% and 35% lower than the wrought CrCoNi alloy at 298 K and 77 K, respectively. Here, the resistance to crack growth of the LPBF CrCoNi from its hierarchical micro- and meso-structures was evaluated using nonlinear-elastic fracture mechanics by measuring R-curve behavior in the form of the J-integral as a function of crack extension. The specific features of the hierarchical microstructures at different length-scales provide a basis for the strengthening and toughening properties of this additively manufactured medium-entropy alloy. This correlation between the deformation and the hierarchical microstructures at different length-scales may provide future guidance for improving the fracture toughness properties of medium-entropy alloys.

36 MATERIALS SCIENCE↗

Multi-variance replica exchange SGMCMC for inverse and forward problems via Bayesian PINN

Physics-informed neural network (PINN) has been successfully applied in solving a variety of nonlinear non-convex forward and inverse problems. However, the training is challenging because of the non-convex loss functions and the multiple optima in the Bayesian inverse problem. In this work, we propose a multi-variance replica exchange stochastic gradient Langevin dynamics method to tackle the challenge of the multiple local optima in the optimization and the challenge of the multiple modal posterior distribution in the inverse problem. Replica exchange methods are capable of escaping from the local traps and accelerating the convergence; two chains with different temperatures are designed where the low temperature chain aims for the local convergence, and the target of the high temperature chain is to travel globally and explore the whole loss function entropy landscape. However, it may not be efficient to solve mathematical inversion problems by using the vanilla replica method directly since the method doubles the computational cost in evaluating the forward solvers (likelihood functions) in the two chains. To address this issue, we propose to make different assumptions on the energy function estimation and this facilities one to use solvers of different fidelities in the likelihood function evaluation. More precisely, one can use a solver with low fidelity in the high temperature chain while using a solver with high fidelity in the low temperature chain. Our proposed method significantly lowers the computational cost in the high temperature chain, meanwhile preserving the accuracy and converging very fast. Here we give an unbiased estimate of the swapping rate and give an estimation of the discretization error of the scheme. To verify our idea, we design and solve four inverse problems which have multiple modes. The proposed method is also employed to train the Bayesian PINN to solve the forward and inverse problems; faster and more accurate convergence has been observed when compared to the stochastic gradient Langevin dynamics (SGLD) method and vanilla replica exchange methods.

97 MATHEMATICS AND COMPUTING↗

Two-fluid and kinetic transport physics of Kelvin–Helmholtz instabilities in nonuniform low-beta plasmas

Hall-magnetohydrodynamic (Hall-MHD) theory, two-fluid simulations, and kinetic simulations are used in this work to investigate the cross-field transport properties of Kelvin–Helmholtz instabilities in nonuniform low-beta collisionless plasmas. Hall-MHD analysis shows how the linear properties of the instability are modified by density gradients and magnetization. High-order accurate two-fluid and kinetic simulations, with complete dynamics of finite-mass electrons and ions, are applied to a suite of parameter cases to systematically assess the effects of diamagnetic drift, magnetization, charge separation, and finite Larmor motion. Initialization of exact two-species kinetic equilibria facilitates the study of isolated physical effects and enables detailed cross-comparisons between two-fluid and kinetic simulations, including for cases where ion gyroradii are comparable to gradient scale lengths. For nonuniform plasmas with significant space charge, the results of two-fluid and kinetic simulations are found to disagree with Hall-MHD predictions. Kelvin–Helmholtz instability growth rates, per unit shear, are shown to be smaller when ion diamagnetic drift and $E \times B$ drift are parallel and larger when the two drifts are antiparallel. The effect is attributed to polarization drift in the shear layer, which leads to redistribution of charge, alters the electric field that drives plasma advection, and consequently modifies growth rates. Instability-induced mass transport for different parameters is characterized in terms of the flux across the shear layer and a simplified diffusion model. Distribution functions from kinetic simulations are shown to deviate substantially from Maxwellian reconstructions, indicating the importance of kinetic physics during the nonlinear phase of the instability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Data-driven Vulnerability Analysis of Networked Pipeline System

This paper introduces an attack generation framework for evaluating the vulnerability of nonlinear networked pipeline systems. The vulnerability analysis is formulated as determining the presence of feasible attack sets, defined by boundary functions representing the effectiveness and stealthiness of attack signals with respect to the objective and attack detection module. The framework utilizes three data-driven models, including two discriminative models that learn the boundary functions and a generative model that produces elements of the feasible attack set. A new loss function ensures successful attack generation with high probability.

03 NATURAL GAS↗

Semi-Lagrangian nodal discontinuous Galerkin method for the BGK model

In this work, we propose a semi-Lagrangian (SL) nodal discontinuous Galerkin (DG) solver for the BGK equation. The BGK model was introduced by Bhatnagar, Gross, and Krook [1] as a relaxation model for the fundamental Boltzmann equation [5], which describes the kinetic dynamic of rarefied gases with a probability distribution function. The challenges of designing efficient numerical schemes for the Boltzmann equation mainly come from its high dimensionality and complicated nonlinear collision operator. The BGK model gains interests since it has much lower computational cost, due to the relatively simple structure of the relaxation operator in replacement of the collision operator, while simultaneously preserving several important physical properties, such as macroscopic quantities and dissipation of entropy.

97 MATHEMATICS AND COMPUTING↗

Stability of distributed parameter systems.

A theorem is derived for the stability of solutions of general linear partial differential equations. A norm of the state space in the form of multiple integrals over the spatial domain is used for the Liapunov functional. Theorems and lemmas are also given for linear time-invariant constant coefficient distributed parameter systems, a class of nonlinear distributed parameter systems and for others with a Lure-type nonlinearity. The theorem conditions are similar to those known for corresponding ordinary differential equations but with operators replacing matrices.

Park, K. E.↗

Research study on stabilization and control. Modern sampled-date control theory. Stability analysis of the low cost large space telescope system

A mathematical model employing Fourier series is used to show quantization and reaction wheel friction nonlinearity in a telescope system for use in space. Block diagrams are used to illustrate the system. A discrete describing function of a quantizer also is given, and input and output signal waveforms, with illustrative examples, are shown.

Kuo, B. C.↗

Prediction of jump phenomena in rotationally-coupled maneuvers of aircraft, including nonlinear aerodynamic effects

An analytical method has been developed for predicting critical control inputs for which nonlinear rotational coupling may cause sudden jumps in aircraft response. The analysis includes the effect of aerodynamics which are nonlinear in angle of attack. The method involves the simultaneous solution of two polynomials in roll rate, whose coefficients are functions of angle of attack and the control inputs. Results obtained using this procedure are compared with calculated time histories to verify the validity of the method for predicting jump-like instabilities.

Young, J. W.↗

Efficiency of unconstrained minimization techniques in nonlinear analysis

Unconstrained minimization algorithms have been critically evaluated for their effectiveness in solving structural problems involving geometric and material nonlinearities. The algorithms have been categorized as being zeroth, first, or second order depending upon the highest derivative of the function required by the algorithm. The sensitivity of these algorithms to the accuracy of derivatives clearly suggests using analytically derived gradients instead of finite difference approximations. The use of analytic gradients results in better control of the number of minimizations required for convergence to the exact solution.

Kamat, M. P.↗

Objective scatterometer wind ambiguity removal using smoothness and dynamical constraints

In the present investigation, a variational analysis method (VAM) is used to remove the ambiguity of the Seasat-A Satellite Scatterometer (SASS) winds. At each SASS data point, two, three, or four wind vectors (termed ambiguities) are retrieved. It is pointed out that the VAM is basically a least squares method for fitting data. The problem may be nonlinear. The best fit to the data and constraints is obtained on the basis of a minimization of the objective function. The VAM was tested and tuned at 12 h GMT Sept. 10, 1978. Attention is given to a case study involving an intense cyclone centered south of Japan at 138 deg E.

Hoffman, R. N.↗

Advanced Rotordynamic Nonlinear Transient Simulation

Advanced rotordynamic nonlinear transient-simulation program, TRANSIM, developed to predict response of high-performance rotating machinery to variety of forcing functions. Works by modal superposition of rotor and casing subsystems. Transient response of system calculated by numerical integration of equations of motion, performed in modal coordinates. Resulting data transformed back into physical coordinates as required to determine user-requested loads and accelerations as function of time. Used to analyze Space Shuttle main engine high-pressure fuel turbopump. TRANSIM written in FORTRAN 77.

Becht, D. G.↗

Statistics of density maxima and the large-scale matter distribution

High peaks in Gaussian noise display enhanced clustering. The enhancement takes two forms: on large scales one obtains a linear amplification of the correlation function which is independent of scale. On smaller scales, but larger than the mass scale of the peaks themselves, a nonlinear (exponential) enhancement of the number density of high peaks in overdense regions arises. The large-scale correlations of Abell's rich clusters can be understood as a manifestation of this phenomenon. If the formation of bright galaxies favors the high overdensity peaks then the number of galaxies (per unit mass) in clusters and groups may be considerably enhanced. Consequences of these ideas for the density parameter and the large-scale matter distribution are discussed.

Kaiser, N.↗

Observational signatures of nonlinear magnetotail particle dynamics

It has been predicted that the nonlinear particle dynamics in the magnetotail leads to a class of resonance structures in the quiet-time ion distribution functions in the central plasma sheet (CPS). These structures exhibit a scaling law of H to the 1/4 power. The first identification of such a scaling law in quiet-time CPS distribution functions obtained aboard ISEE 1 is reported. A method is proposed which uses the observed resonance structures to determine the quiet-time current sheet thickness based on a measurement of the distribution function and magnetic field obtained by one satellite.

Chen, James↗

Optimum combinations of visible and near-infrared reflectances for estimating the fraction of photosynthetically available radiation absorbed by plants

A useful parameter to estimate terrestrial primary productivity, that can be sensed from space, is the daily averaged fraction of Photosynthetically Available Radiation (PAR) absorbed by plants. To evaluate this parameter, investigators have relied on the fact that the relative amount of radiation reflected by a vegetated surface in the visible and near infrared depends on the fraction of the surface covered by the vegetation and therefore, correlates with absorbed PAR. They have used vegetation indices, namely normalized difference and simple ratio, to derive absorbed PAR. The problem with normalized difference and simple ratio is first, they are non linear functions of radiance or reflectance and therefore, cannot be readily applied to heterogeneous targets, second, they are used in generally nonlinear relationships, which make time integrals of the indices not proportional to primary productivity, and third, the relationships depend strongly on the type of canopy and background. To remove these limitations, linear combinations of visible and near infrared reflectances at optimum (one or two) viewing zenith angles are proposed.

Podaire, Alain↗

Neural Network and Regression Approximations in High Speed Civil Transport Aircraft Design Optimization

Nonlinear mathematical-programming-based design optimization can be an elegant method. However, the calculations required to generate the merit function, constraints, and their gradients, which are frequently required, can make the process computational intensive. The computational burden can be greatly reduced by using approximating analyzers derived from an original analyzer utilizing neural networks and linear regression methods. The experience gained from using both of these approximation methods in the design optimization of a high speed civil transport aircraft is the subject of this paper. The Langley Research Center's Flight Optimization System was selected for the aircraft analysis. This software was exercised to generate a set of training data with which a neural network and a regression method were trained, thereby producing the two approximating analyzers. The derived analyzers were coupled to the Lewis Research Center's CometBoards test bed to provide the optimization capability. With the combined software, both approximation methods were examined for use in aircraft design optimization, and both performed satisfactorily. The CPU time for solution of the problem, which had been measured in hours, was reduced to minutes with the neural network approximation and to seconds with the regression method. Instability encountered in the aircraft analysis software at certain design points was also eliminated. On the other hand, there were costs and difficulties associated with training the approximating analyzers. The CPU time required to generate the input-output pairs and to train the approximating analyzers was seven times that required for solution of the problem.

Patniak, Surya N.↗

Numerical Technique for Analyzing Rotating Rake Mode Measurements in a Duct With Passive Treatment and Shear Flow

A technique is presented for the analysis of measured data obtained from a rotating microphone rake system. The system is designed to measure the interaction modes of ducted fans. A Fourier analysis of the data from the rotating system results in a set of circumferential mode levels at each radial location of a microphone inside the duct. Radial basis functions are then least-squares fit to this data to obtain the radial mode amplitudes. For ducts with soft walls and mean flow, the radial basis functions must be numerically computed. The linear companion matrix method is used to obtain both the eigenvalues of interest, without an initial guess, and the radial basis functions. The governing equations allow for the mean flow to have a boundary layer at the wall. In addition, a nonlinear least-squares method is used to adjust the wall impedance to best fit the data in an attempt to use the rotating system as an in-duct wall impedance measurement tool. Simulated and measured data are used to show the effects of wall impedance and mean flow on the computed results.

Dahl, Milo D.↗

Shell Models of RMHD Turbulence and the Heating of Solar Coronal Loops

A simplified nonlinear numerical model for the development of incompressible magnetohydrodynamics in the presence of a strong magnetic field B|| and stratification, nicknamed 'Shell-Atm,' is presented. In planes orthogonal to the mean field, the nonlinear incompressible dynamics is replaced by two-dimensional shell models for the complex variables u and b, allowing one to reach large Reynolds numbers while at the same time carrying out sufficiently long integrations to obtain good statistics at moderate computational cost. The shell models of different planes are coupled by Alfve'n waves propagating along B||. The model may be applied to open or closed magnetic field configurations where the axial field dominates and the plasma pressure is low; here we apply it to the specific case of a magnetic loop of the solar corona heated by means of turbulence driven by photospheric motions, and we use statistics for its analysis. The Alfven waves interact nonlinearly and form turbulent spectra in the directions perpendicular and, through propagation, also parallel to the mean field. A heating function is obtained and shown to be intermittent; the average heating is consistent with values required for sustaining a hot corona and is proportional to the aspect ratio of the loop to the -1.5 power, and haracteristic properties of heating events are distributed as power laws. Crosscorrelations show a delay of dissipation compared with energy content.

corona↗