Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “stochastic methods”

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 1,189 records · Page 66
All sourcesNASA NTRSDOE OSTI
DOE OSTI2012

Zgoubi Users' Guide

The computer code zgoubi calculates trajectories of charged particles in magnetic and electric fields. At the origin specially adapted to the definition and adjustment of beam lines and magnetic spectrometers, it has so evolved that it allows the study of systems including complex sequences of optical elements such as dipoles, quadrupoles, arbitrary multipoles, FFAG magnets and other magnetic or electric devices, and is able as well to handle periodic structures. Compared to other codes, it presents several peculiarities, as follows - a non-exhaustive list : • a numerical method for integrating the Lorentz equation, based on Taylor series, which optimizes computing time and provides high accuracy and strong symplecticity, • spin tracking, using the same numerical method as for the Lorentz equation, • account of stochastic photon emission, and its effects on particle dynamics, • calculation of the synchrotron radiation electric field and spectra in arbitrary magnetic fields, from the ray-tracing outcomes, • the possibility of using a mesh, which allows ray-tracing from simulated or measured (1-D, 2-D or 3-D) electric and magnetic field maps, • a number Monte Carlo procedures : unlimited number of trajectories, in-flight decay, stochastic radiation, etc., • built-in fitting procedures allowing arbitrary variables and a large variety of constraints, easily expandable, • multi-turn tracking in circular accelerators including features proper to machine parameter calculation and survey, • simulation of time-varying power supplies, and • simulation of arbitrary radio-frequency programs. The initial version of zgoubi was dedicated to ray-tracing in magnetic elements, beam lines, spectrometers. It was perfected for the purpose of studying, and operating, the four spectrometers SPES I, II, III, IV at the Laboratoire National SATURNE (CEA-Saclay, France), and, later, SPEG at GANIL (Caen, France). Developments regarding spin tracking and ray-tracing in combined electric and magnetic fields were implemented, in the late 1980s and early 1990s respectively. In the mid-1990s, the computation of synchrotron radiation electromagnetic impulse and spectra was introduced, for the purpose of synchrotron radiation diagnostic R&D at LEP, and further applied to the design of the SR diagnostics installations at LHC in the early 2000s. In the mean time, several new optical elements were added, such as electro-magnetic and other electrostatic lenses. Used since several years for special studies in periodic machines (e.g., SATURNE at Saclay, COSY at Julich, LEP and LHC at CERN), zgoubi has also undergone extensive developments regarding storage ring related features. Many developments have been accomplished since the early 2000s in the frame of a number of project design and beam dynamics studies, as the neutrino factory, lepton and hadron colliders, spin studies at AGS and RHIC, etc. As a consequence the list of optical elements and the compendium of numerical methods, so-called “Glossary of Keywords” list, pp. 7 and 169, has stretched with new simulation and computing procedures, ranging from fitting (FIT2 procedure ; additional constraints) to overlapping magnetic field capabilities (DIPOLES, FFAG), spin manipulation (SPINR), optical elements (BEAMBEAM), radiation damping tools (SRLOSS) and many others (FAISTORE, MAP2D-E, OPTICS, PICKUPS, TWISS, etc.). The graphic interface to zgoubi (zpop, Part D) has undergone extensive developments, making it a convenient companion tool to the use of zgoubi.

43 PARTICLE ACCELERATORS↗
NASA NTRS2016

A DSMC Surface Chemistry Model for Carbon-Based Ablators

A detailed molecular surface chemistry model for the DSMC (Direct Simulation Monte Carlo) method is proposed and implemented into the SPARTA (Stochastic PArallel Rarefied-gas Time-accurate Analyzer) DSMC solver. Molchanova et al. constructed a molecular model for surface recombination in DSMC that includes different surface processes (adsorption, desoprtion, Eley-Rideal and Langmuir-Hinshelwood). All surface processes can be divided into two groups: surface mechanisms, which involve only the particle adsorbed by the surface (desorption and Langmuir-Hinshelwood), and impact mechanisms, which also involve gas-phase particles (adsorption, Eley-Rideal). Using a similar approach, the 14-reaction kinetic model of oxygen-carbon interaction suggested by Zhlukhtov and Abe, as well as more recent models by Alba et al., Poovathinghal et al., and a new model developed in the scope of this work, are implemented in SPARTA. The computational results for the different oxidation models are compared with experimental results from Murray et al. (oxidation of a vitreous carbon surface due to a hyperthermal beam of O and O2), with a particular focus on fluxes, angular and Time-Of-Flight distributions of scattered particles.

oxidation↗
DOE OSTI2024

A Kaczmarz-inspired approach to accelerate the optimization of neural network wavefunctions

Neural network wavefunctions optimized using the variational Monte Carlo method have been shown to produce highly accurate results for the electronic structure of atoms and small molecules, but the high cost of optimizing such wavefunctions prevents their application to larger systems. We propose the Subsampled Projected-Increment Natural Gradient Descent (SPRING) optimizer to reduce this bottleneck. SPRING combines ideas from the recently introduced minimum-step stochastic reconfiguration optimizer (MinSR) and the classical randomized Kaczmarz method for solving linear least-squares problems. We demonstrate that SPRING outperforms both MinSR and the popular Kronecker-Factored Approximate Curvature method (KFAC) across a number of small atoms and molecules, given that the learning rates of all methods are optimally tuned. For example, on the oxygen atom, SPRING attains chemical accuracy after forty thousand training iterations, whereas both MinSR and KFAC fail to do so even after one hundred thousand iterations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Stochastics and EUV Patterning in the 1x-nm Regime

The problem of stochastics in photoresist patterning is gaining increased attention. Understanding this problem requires new modeling methods. Here we describe the use of the Multivariate Poisson Propagation Model (MPPM) to study the relative importance of a variety of stochastic terms in both chemically amplified and non-chemically amplified resists. The results show that for the chemically amplified case, materials stochastic effects are on par with photon stochastics effects. The model is used to study both line-width roughness (LWR) impacts as well as contact size variations (CDU). As one might expect, contact CDU follows the same trends as LWR, but places even more sever constraints on the stochastic terms when considering the same feature size. Noting the contact patterning challenge, we also describe a phase-shift mask patterning method enabling the photon effect to be greatly reduced. At equivalent CDU, we demonstrate an effective 7x reduction in required source dose when patterning 25-nm half pitch contacts.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Tuning structure and mobility of solvation shells surrounding tracer additives

Molecular dynamics simulations and a stochastic Fokker-Planck equation based approach are used to illuminate how position-dependent solvent mobility near one or more tracer particle(s) is affected when tracer-solvent interactions are rationally modified to affect corresponding solvation structure. For tracers in a dense hard-sphere fluid, we compare two types of tracer-solvent interactions: (1) a hard-sphere-like interaction, and (2) a soft repulsion extending beyond the hard core designed via statistical mechanical theory to enhance tracer mobility at infinite dilution by suppressing coordination-shell structure [Carmer et al., Soft Matter 8, 4083–4089 (2012)]. For the latter case, we show that the mobility of surrounding solvent particles is also increased by addition of the soft repulsive interaction, which helps to rationalize the mechanism underlying the tracer’s enhanced diffusivity. However, if multiple tracer surfaces are in closer proximity (as at higher tracer concentrations), similar interactions that disrupt local solvation structure instead suppress the position-dependent solvent dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Revisiting stochastic variability of AGNs with structure functions

Discrepancies between reported structure function (SF) slopes and their overall flatness as compared to the expectations from the damped random walk (DRW) model, which generally well describes the variability of active galactic nuclei (AGNs), have triggered us to study this problem in detail. We review common AGN variability observables and identify their most common problems. Equipped with this knowledge, we study ∼9000 r-band AGN light curves from Stripe 82 of the Sloan Digital Sky Survey, using SFs described by stochastic processes with the power exponential covariance matrix of the signal. We model the “subensemble” SFs in the redshift–absolute magnitude bins with the full SF equation (including the turnover and the noise part) and a single power law (SPL; in the “red noise regime” after subtracting the noise term). The distribution of full-equation SF (SPL) slopes peaks at γ=0.55±0.08 (0.52 ± 0.06) and is consistent with the DRW model. There is a hint of a weak correlation of γ with the luminosity and a lack of correlation with the black hole mass. The typical decorrelation timescale in the optical is τ=0.97±0.46 year. The SF amplitude at one year obtained from the SPL fitting is SF{sub 0}=0.22±0.06 mag and is overestimated because the SF is already at the turnover part, so the true value is SF{sub 0}=0.20±0.06 mag. The asymptotic variability is SF{sub ∞}=0.25±0.06 mag. It is strongly anticorrelated with both the luminosity and the Eddington ratio and is correlated with the black hole mass. The reliability of these results is fortified with Monte Carlo simulations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Full-dispersion Monte Carlo simulation of phonon transport in micron-sized graphene nanoribbons

We simulate phonon transport in suspended graphene nanoribbons (GNRs) with real-space edges and experimentally relevant widths and lengths (from submicron to hundreds of microns). The full-dispersion phonon Monte Carlo simulation technique, which we describe in detail, involves a stochastic solution to the phonon Boltzmann transport equation with the relevant scattering mechanisms (edge, three-phonon, isotope, and grain boundary scattering) while accounting for the dispersion of all three acoustic phonon branches, calculated from the fourth-nearest-neighbor dynamical matrix. We accurately reproduce the results of several experimental measurements on pure and isotopically modified samples [S. Chen et al., ACS Nano 5, 321 (2011);S. Chen et al., Nature Mater. 11, 203 (2012); X. Xu et al., Nat. Commun. 5, 3689 (2014)]. We capture the ballistic-to-diffusive crossover in wide GNRs: room-temperature thermal conductivity increases with increasing length up to roughly 100 μm, where it saturates at a value of 5800 W/m K. This finding indicates that most experiments are carried out in the quasiballistic rather than the diffusive regime, and we calculate the diffusive upper-limit thermal conductivities up to 600 K. Furthermore, we demonstrate that calculations with isotropic dispersions overestimate the GNR thermal conductivity. Zigzag GNRs have higher thermal conductivity than same-size armchair GNRs, in agreement with atomistic calculations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

The application of wavelet shrinkage denoising to magnetic Barkhausen noise measurements

The application of Magnetic Barkhausen Noise (MBN) as a non-destructive method of defect detection has proliferated throughout the manufacturing community. Instrument technology and measurement methodology have matured commensurately as applications have moved from the R and D labs to the fully automated manufacturing environment. These new applications present a new set of challenges including a bevy of error sources. A significant obstacle in many industrial applications is a decrease in signal to noise ratio due to (i) environmental EMI and (II) compromises in sensor design for the purposes of automation. The stochastic nature of MBN presents a challenge to any method of noise reduction. An application of wavelet shrinkage denoising is proposed as a method of decreasing extraneous noise in MBN measurements. The method is tested and yields marked improvement on measurements subject to EMI, grounding noise, and even measurements in ideal conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Uncertainty quantification in scientific machine learning: Methods, metrics, and comparisons

Neural networks (NNs) are currently changing the computational paradigm on how to combine data with mathematical laws in physics and engineering in a profound way, tackling challenging inverse and ill-posed problems not solvable with traditional methods. However, quantifying errors and uncertainties in NN-based inference is more complicated than in traditional methods. This is because in addition to aleatoric uncertainty associated with noisy data, there is also uncertainty due to limited data, but also due to NN hyperparameters, overparametrization, optimization and sampling errors as well as model misspecification. Although there are some recent works on uncertainty quantification (UQ) in NNs, there is no systematic investigation of suitable methods towards quantifying the total uncertainty effectively and efficiently even for function approximation, and there is even less work on solving partial differential equations and learning operator mappings between infinite-dimensional function spaces using NNs. In this work, we present a comprehensive framework that includes uncertainty modeling, new and existing solution methods, as well as evaluation metrics and post-hoc improvement approaches. Further, to demonstrate the applicability and reliability of our framework, we present an extensive comparative study in which various methods are tested on prototype problems, including problems with mixed input-output data, and stochastic problems in high dimensions. In the Appendix, we include a comprehensive description of all the UQ methods employed. Further, to help facilitate the deployment of UQ in Scientific Machine Learning research and practice, we present and develop in [1] an open-source Python library (github.com/Crunch-UQ4MI/neuraluq), termed NeuralUQ, that is accompanied by an educational tutorial and additional computational experiments.

11 physics-informed neural networks↗
DOE OSTI2015

Exnihilo Transport Methods Manuals Revision 0

Exnihilo is a transport code system that contains both deterministic and stochastic (Monte Carlo) solvers. The deterministic solvers are contained in the Denovo package while the Monte Carlo solvers are implemented in the Shift package. This document explains the mathematical and numerical methods employed within Exnihilo. It is not a users guide, nor is it a code developer's manual. Naturally, there is cross-over between the code implementation and mathematical description of any given method, and these are included for the purpose of greater understanding where appropriate. The purpose of this document is to formally describe the equations that are solved by the various packages inside of Exnihilo. In general, linkages are not made between a given numerical method and the Exnihilo code base. This is largely due to the fact that the Exnihilo code base changes far more rapidly than the actual methods that it is solving. Thus, this documentation would go rapidly out of date if cross-references were made between the methods and the code that implements them. Instead, developers are encouraged to look at the Doxygen-produced code documentation that explains what each translation unit in the code is doing. Where necessary we will make distinctions between methods that are implemented in Exnihilo and methods that are documented to provide better understanding of the broader field and provide context for the chosen methods in Exnihilo.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

Role of atomistic structure in the stochastic nature of conductivity in substoichiometric tantalum pentoxide

First-principles calculations of electrical conductivity (σ{sub o}) are revisited to determine the atomistic origin of its stochasticity in a distribution generated from sampling 14 ab-initio molecular dynamics configurations from 10 independently quenched models (n = 140) of substoichiometric amorphous Ta{sub 2}O{sub 5}, where each structure contains a neutral O monovacancy (V{sub O}{sup 0}). Structural analysis revealed a distinct minimum Ta-Ta separation (dimer/trimer) corresponding to each V{sub O}{sup 0} location. Bader charge decomposition using a commonality analysis approach based on the σ{sub o} distribution extremes revealed nanostructural signatures indicating that both the magnitude and distribution of cationic charge on the Ta subnetwork have a profound influence on σ{sub o}. Furthermore, visualization of local defect structures and their electron densities reinforces these conclusions and suggests σ{sub o} in the amorphous oxide is best suppressed by a highly charged, compact Ta cation shell that effectively screens and minimizes localized V{sub O}{sup 0} interaction with the a-Ta{sub 2}O{sub 5} network; conversely, delocalization of V{sub O}{sup 0} corresponds to metallic character and high σ{sub o}. The random network of a-Ta{sub 2}O{sub 5} provides countless variations of an ionic configuration scaffold in which small perturbations affect the electronic charge distribution and result in a fixed-stoichiometry distribution of σ{sub o}; consequently, precisely controlled and highly repeatable oxide fabrication processes are likely paramount for advancement of resistive memory technologies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Quantifying the Uncertainty in Deterministic Phonon Transport Calculations of Thermal Conductivity using Polynomial Chaos Expansions

The nature of computational simulations requires the inclusion of an uncertainty analysis, as we have limited knowledge of all physically determined input parameters for a computationally simulated problem. We rely on uncertainty quantification (UQ) to characterize our confidence in the outcomes. Quantifying uncertainty can provide a basis for certifications in high-consequence decisions, such as nuclear reactor design, and is a fundamental component of model validation. We employ a previously developed method of uncertainty quantification, polynomial chaos expansion with stochastic collocation (PCE-SC), applied to deterministic phonon transport simulations. In these simulations, we use the neutron transport code Rattlesnake, which solves the Self-Adjoint Angular Flux (SAAF) formulation of the transport equation with a continuous finite element (CFEM) spatial discretization and discrete ordinates, spherical harmonics angular discretizations. Rattlesnake was developed in the multi-physics object oriented simulation environment (MOOSE) framework. We have previously shown Rattlesnake to be effective in simulating phonon transport. We aim to provide a deterministic phonon transport framework for heterogeneous nuclear fuel with fission product defects to predict thermal conductivity (?). A first principles, physics-based calculation of thermal conductivity must involve factors such as the microstructure of nuclear fuel, which constantly changes during the fission process through the formation of isotopic decay products. Heat transport in oxide nuclear fuels is dominated by phonon transport. Impurities in the bulk material influence the transport of energy at the fundamental level, altering the scattering behavior of phonons and electrons. Conventionally, heat transport follows classical physics based on the heat equation derived from Fourier's law q = -k∇T, where q is heat flux, k is thermal conductivity and ∇T is a temperature gradient. However, Fourier's law is a macroscopic empirical law in which the thermal conductivity? does not have a mechanistic connection to the underpinning heat transport processes. Thermal conductivity of a material depends both on the material's intrinsic ability to transport heat and a variety of resistive effects caused by defects in the material. Thus ab initio prediction of the macroscopic conductivity - the property of interest for safe reactor operation - requires simulating detailed processes of heat transport, and then determining the effective thermal conductivity of the simulated material from the resulting heat flux under the imposed temperature difference. The thermal conductivity of a bulk, homogeneous, dielectric material can be well estimated by the mechanistically derived expression: k{sub bulk} = 1/3 C{sub ν}νgλ (2), where C{sub ν}, νg, and λ are the volumetric specific heat, phonon speed, and phonon mean free path, respectively. In these problems the relevant parameter is the material's acoustic thickness, its characteristic distance L relative to the phonon mean free path λ. In Eq. (2) the largest source of uncertainty is λ. While propagating uncertainty in λ to uncertainty in k through Eq. (2) is trivial, systems with extrinsic scattering require more sophisticated approaches. At the microscopic level, uncertainty in λ changes both a material's intrinsic thermal conductivity. Our goal is to propagate the uncertainty in λ through the deterministic transport computation of k. Because there are a small number of uncertain input quantities, we use the method of polynomial chaos expansion (PCE), which expresses solutions in the form of spectral expansions of an uncertain variable. This approach combines both intrusive and nonintrusive methods of uncertainty propagation techniques and results in a unique formulation which is very effective and efficient for problems with few uncertain parameters. Uncertainty Quantification and Sensitivity Analysis We use PCE-SC to measure propagation of uncertainty in a 3-D phonon transport problem of homogeneous silicon, to compute the mean and variance in temperature, heat flux and thermal conductivity. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2016

Analysis of isothermal and cooling-rate-dependent immersion freezing by a unifying stochastic ice nucleation model

Immersion freezing is an important ice nucleation pathway involved in the formation of cirrus and mixed-phase clouds. Laboratory immersion freezing experiments are necessary to determine the range in temperature, T , and relative humidity, RH, at which ice nucleation occurs and to quantify the associated nucleation kinetics. Typically, isothermal (applying a constant temperature) and cooling-rate-dependent immersion freezing experiments are conducted. In these experiments it is usually assumed that the droplets containing ice nucleating particles (INPs) all have the same INP surface area (ISA); however, the validity of this assumption or the impact it may have on analysis and interpretation of the experimental data is rarely questioned. Descriptions of ice active sites and variability of contact angles have been successfully formulated to describe ice nucleation experimental data in previous research; however, we consider the ability of a stochastic freezing model founded on classical nucleation theory to reproduce previous results and to explain experimental uncertainties and data scatter. A stochastic immersion freezing model based on first principles of statistics is presented, which accounts for variable ISA per droplet and uses parameters including the total number of droplets, N tot , and the heterogeneous ice nucleation rate coefficient, J het ( T ). This model is applied to address if (i) a time and ISA-dependent stochastic immersion freezing process can explain laboratory immersion freezing data for different experimental methods and (ii) the assumption that all droplets contain identical ISA is a valid conjecture with subsequent consequences for analysis and interpretation of immersion freezing. The simple stochastic model can reproduce the observed time and surface area dependence in immersion freezing experiments for a variety of methods such as: droplets on a cold-stage exposed to air or surrounded by an oil matrix, wind and acoustically levitated droplets, droplets in a continuous-flow diffusion chamber (CFDC), the Leipzig aerosol cloud interaction simulator (LACIS), and the aerosol interaction and dynamics in the atmosphere (AIDA) cloud chamber. Observed time-dependent isothermal frozen fractions exhibiting non-exponential behavior can be readily explained by this model considering varying ISA. An apparent cooling-rate dependence of J het is explained by assuming identical ISA in each droplet. When accounting for ISA variability, the cooling-rate dependence of ice nucleation kinetics vanishes as expected from classical nucleation theory. Finally, the model simulations allow for a quantitative experimental uncertainty analysis for parameters N tot , T , RH, and the ISA variability. We discuss the implications of our results for experimental analysis and interpretation of the immersion freezing process.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Quantum Monte Carlo benchmarking of large noncovalent complexes in the L7 benchmark set

We have used diffusion Monte Carlo (DMC) to perform calculations on the L7 benchmark set. DMC is a stochastic numerical integration scheme in real-space and part of a larger set of quantum Monte Carlo methods. The L7 set was designed to test the ability of electronic structure methods to include dispersive interactions. While the agreement between DMC and quantum-chemical state-of-the-art methods is excellent for some of the structures, there are significant differences in others. In contrast to wavefunction-based quantum chemical methods, DMC is a first-principle many-body method with the many-body wavefunction evolving in real space. It includes explicitly all electron–electron interactions and is relatively insensitive to the size of the basis set.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Sliced-Inverse-Regression--Aided Rotated Compressive Sensing Method for Uncertainty Quantification

Compressive-sensing-based uncertainty quantification methods have become a pow- erful tool for problems with limited data. In this paper, we use the sliced inverse regression (SIR) method to provide an initial guess for the alternating direction method, which is used to enhance sparsity of the Hermite polynomial expansion of stochastic state variables. The sparsity improvement increases both the efficiency and accuracy of the compressive-sensing-based uncertainty quantification method. We demonstrate that the initial guess from SIR is more suitable for the cases when the available data is very limited (Algorithm 4). We also propose another algorithm (Algorithm 5) that performs dimension reduction first with sliced inverse regression, then constructs a Hermite polynomial expansion of the reduced model. This method allows us to approximate the statistics accurately with even less available data. Both methods are non-intrusive and require no a priori information of the sparsity of the system. We demonstrate the effectiveness of these two methods (Algorithms 4 and 5) using problems with up to 500 random dimensions.

Yang, Xiu↗
DOE OSTI2020

Scenario Creation and Power-Conditioning Strategies for Operating Power Grids with Two-Stage Stochastic Economic Dispatch: Preprint

A significant difficultly associated with the use of stochastic programming to solve optimal power flow problems on a 5-minute timescale is the quality of renewable energy scenarios input by the user. This is especially true when considering power systems with high penetrations of renewable energy, e.g. wind power. This paper introduces the use of stochastic programming to solve the DCOPF problem with scenarios drawn directly from high-fidelity data sets. Hence, the proposed method avoids the problem of lost physics by finding high-fidelity analogs that can describe future states of the system. Furthermore, this method can be simply extended to output multi-period scenarios to the stochastic program. We demonstrate the effectiveness of this technique on simulated dispatch operations of the RTS-GMLC over a week.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2004

Scatter in Carbon/Silicon Carbide (C/SiC) Composites Quantified

Carbon-fiber-reinforced silicon carbide matrix (C/SiC) composites processed by chemical vapor infiltration are candidate materials for aerospace thermal structures. Carbon fibers can retain properties at very high temperatures, but they are known to have poor oxidation resistance in adverse, high-temperature environments. Nevertheless, the combination of CVI-SiC matrix with higher stiffness and oxidation resistance, the interfacial coating, and additional surface-seal coating provides the necessary protection to the carbon fibers, and makes the material viable for high-temperature space applications operating under harsh environments. Furthermore, C/SiC composites, like other ceramic matrix composites (CMCs), exhibit graceful non-catastrophic failure because of various inherent energy dissipating mechanisms. The material exhibits nonlinearity in deformation even at very low stress levels. This is the result of the severe matrix microcracking present in the as processed composite because of large differences between the coefficients of thermal expansion of the fiber and the matrix. Utilization of these advanced composites in next generation space vehicles will require innovative structural configurations, updated materials, and refined analyses. Structural safety issues for these vehicles are in direct competition with performance and cost. One would have to quantify the uncertainties associated with the design using formal probabilistic methods. Specifically four fundamental aspects on which analyses are based-- (1) loading conditions, (2) material behavior, (3) geometrical configurations, and (4) structural connections between the composite components and baseline structure--are stochastic in nature. A direct way to formally account for uncertainties is to develop probabilistic structural analysis methods where all participating variables are described by appropriate probability density functions. The present work, however, focuses on analyzing the stochastic material behavior of these advanced composites using formal probabilistic analysis methods. Often, some of the desirable property characteristics that allow composites to offer advantages over conventional structural materials (like tailoring of composite properties) and the complexity are in fact responsible for their greater statistical variability and the requirements for more characterization tests. Composite properties are anisotropic as well, having different properties in different directions. This means that characterization of a property such as stiffness--which will vary greatly depending on the orientation of the fiber relative to the direction of the testing--must be repeated for several different directions and loading conditions. The fabrication process for composites also introduces statistical variations in properties and geometry. A composite part is produced in a number of steps, each of which introduces statistical variability. The matrix is usually produced from a combination of raw materials; and the fiber, which has its own set of properties, is often coated or surface treated, introducing yet another source of variability.

Murthy, Pappu L. N.↗
DOE OSTI2014

On the equivalence of dynamically orthogonal and bi-orthogonal methods: Theory and numerical simulations

The Karhunen–Lòeve (KL) decomposition provides a low-dimensional representation for random fields as it is optimal in the mean square sense. Although for many stochastic systems of practical interest, described by stochastic partial differential equations (SPDEs), solutions possess this low-dimensional character, they also have a strongly time-dependent form and to this end a fixed-in-time basis may not describe the solution in an efficient way. Motivated by this limitation of standard KL expansion, Sapsis and Lermusiaux (2009) [26] developed the dynamically orthogonal (DO) field equations which allow for the simultaneous evolution of both the spatial basis where uncertainty ‘lives’ but also the stochastic characteristics of uncertainty. Recently, Cheng et al. (2013) [28] introduced an alternative approach, the bi-orthogonal (BO) method, which performs the exact same tasks, i.e. it evolves the spatial basis and the stochastic characteristics of uncertainty. In the current work we examine the relation of the two approaches and we prove theoretically and illustrate numerically their equivalence, in the sense that one method is an exact reformulation of the other. We show this by deriving a linear and invertible transformation matrix described by a matrix differential equation that connects the BO and the DO solutions. We also examine a pathology of the BO equations that occurs when two eigenvalues of the solution cross, resulting in an instantaneous, infinite-speed, internal rotation of the computed spatial basis. We demonstrate that despite the instantaneous duration of the singularity this has important implications on the numerical performance of the BO approach. On the other hand, it is observed that the BO is more stable in nonlinear problems involving a relatively large number of modes. Several examples, linear and nonlinear, are presented to illustrate the DO and BO methods as well as their equivalence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗