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At least 127 records · Page 7

Multiscale Modeling of Intergranular Fracture in Aluminum: Constitutive Relation For Interface Debonding

Intergranular fracture is a dominant mode of failure in ultrafine grained materials. In the present study, the atomistic mechanisms of grain-boundary debonding during intergranular fracture in aluminum are modeled using a coupled molecular dynamics finite element simulation. Using a statistical mechanics approach, a cohesive-zone law in the form of a traction-displacement constitutive relationship, characterizing the load transfer across the plane of a growing edge crack, is extracted from atomistic simulations and then recast in a form suitable for inclusion within a continuum finite element model. The cohesive-zone law derived by the presented technique is free of finite size effects and is statistically representative for describing the interfacial debonding of a grain boundary (GB) interface examined at atomic length scales. By incorporating the cohesive-zone law in cohesive-zone finite elements, the debonding of a GB interface can be simulated in a coupled continuum-atomistic model, in which a crack starts in the continuum environment, smoothly penetrates the continuum-atomistic interface, and continues its propagation in the atomistic environment. This study is a step towards relating atomistically derived decohesion laws to macroscopic predictions of fracture and constructing multiscale models for nanocrystalline and ultrafine grained materials.

Yamakov, V.↗

Statistical mechanics of 'negative temperature' states

Consideration of the dynamics of a two-dimensional guiding center plasma, recently shown by Taylor and McNamara (1971) to be identical to the dynamics of the discrete vortex model of Onsager (1949). A semirigorous application of the methods of equilibrium statistical mechanics to the guiding center plasma (or equivalently, the line vortex system) is presented. An adaptation of the apparatus of the theory of probability is attempted, in the form given by Khinchin (1949) to obtain ensemble-average predictions for the states of the guiding center plasma. Interest focuses primarily on the regime in which the interaction energy is high enough to be above the Onsager 'negative temperature' threshold.

Montgomery, D.↗

Analytical methods for superresolution dislocation identification in dark-field X-ray microscopy

In this work, we develop several inference methods to estimate the position of dislocations from images generated using dark-field X-ray microscopy (DFXM)—achieving superresolution accuracy and principled uncertainty quantification. Using the framework of Bayesian inference, we incorporate models of the DFXM contrast mechanism and detector measurement noise, along with initial position estimates, into a statistical model coupling DFXM images with the dislocation position of interest. We motivate several position estimation and uncertainty quantification algorithms based on this model. We then demonstrate the accuracy of our primary estimation algorithm on synthetic realistic DFXM images of edge dislocations in single-crystal aluminum. We conclude with a discussion of our methods’ impact on future dislocation studies and possible future research avenues.

36 MATERIALS SCIENCE↗

2023 Roadmap on molecular modelling of electrochemical energy materials

New materials for electrochemical energy storage and conversion are the key to the electrification and sustainable development of our modern societies. Molecular modelling based on the principles of quantum mechanics and statistical mechanics as well as empowered by machine learning techniques can help us to understand, control and design electrochemical energy materials at atomistic precision. Therefore, this roadmap, which is a collection of authoritative opinions, serves as a gateway for both the experts and the beginners to have a quick overview of the current status and corresponding challenges in molecular modelling of electrochemical energy materials for batteries, supercapacitors, CO 2 reduction reaction, and fuel cell applications.

25 ENERGY STORAGE↗

A hybrid data–model approach to map soil thickness in mountain hillslopes

Abstract. Soil thickness plays a central role in the interactions between vegetation, soils, and topography, where it controls the retention and release of water, carbon, nitrogen, and metals. However, mapping soil thickness, here defined as the mobile regolith layer, at high spatial resolution remains challenging. Here, we develop a hybrid model that combines a process-based model and empirical relationships to estimate the spatial heterogeneity of soil thickness with fine spatial resolution (0.5 m). We apply this model to two aspects of hillslopes (southwest- and northeast-facing, respectively) in the East River watershed in Colorado. Two independent measurement methods – auger and cone penetrometer – are used to sample soil thickness at 78 locations to calibrate the local value of unconstrained parameters within the hybrid model. Sensitivity analysis using the hybrid model reveals that the diffusion coefficient used in hillslope diffusion modeling has the largest sensitivity among all input parameters. In addition, our results from both sampling and modeling show that, in general, the northeast-facing hillslope has a deeper soil layer than the southwest-facing hillslope. By comparing the soil thickness estimated between a machine-learning approach and this hybrid model, the hybrid model provides higher accuracy and requires less sampling data. Modeling results further reveal that the southwest-facing hillslope has a slightly faster surface soil erosion rate and soil production rate than the northeast-facing hillslope, which suggests that the relatively less dense vegetation cover and drier surface soils on the southwest-facing slopes influence soil properties. With seven parameters in total for calibration, this hybrid model can provide a realistic soil thickness map with a relatively small amount of sampling dataset comparing to machine-learning approach. Integrating process-based modeling and statistical analysis not only provides a thorough understanding of the fundamental mechanisms for soil thickness prediction but also integrates the strengths of both statistical approaches and process-based modeling approaches.

58 GEOSCIENCES↗

Strongly magnetized classical plasma models

The class of plasma processes for which the so-called Vlasov approximation is inadequate is investigated. Results from the equilibrium statistical mechanics of two-dimensional plasmas are derived. These results are independent of the presence of an external dc magnetic field. The nonequilibrium statistical mechanics of the electrostatic guiding-center plasma, a two-dimensional plasma model, is discussed. This model is then generalized to three dimensions. The guiding-center model is relaxed to include finite Larmor radius effects for a two-dimensional plasma.

Montgomery, D. C.↗

A Statistical Comparison of PSC Model Simulations and POAM Observations

A better knowledge of PSC composition and formation mechanisms is important to better understand and predict stratospheric ozone depletion. Several past studies have attempted to compare modeling results with satellite observations. These comparisons have concentrated on case studies. In this paper we adopt a statistical approach. POAM PSC observations from several Arctic winters are categorized into Type Ia and Ib PSCs using a technique based on Strawa et al. The discrimination technique has been modified to employ the wavelengths dependence of the extinction signal at all wavelengths rather than only at 603 and 10 18 nm. Winter-long simulations for the 1999-2000 Arctic winter have been made using the IMPACT model. These simulations have been constrained by aircraft observations made during the SOLVE/THESEO 2000 campaign. A complete set of winter-long simulations was run for several different microphysical and PSC formation scenarios. The simulations give us perfect knowledge of PSC type (Ia, Ib, or II), composition, especially condensed phase HNO3 which is important for denitrification, and condensed phase H2O. Comparisons are made between the simulation and observation of PSC extinction at 1018 rim versus wavelength dependence, winter-long percentages of Ia and Ib occurrence, and temporal and altitude trends of the PSCs. These comparisons allow us to comment on how realistic some modeling scenarios are.

Strawa, A. W.↗

Using statistical modeling to predict and understand fusion experiments

Over 300 cryogenic layered direct-drive inertial confinement fusion implosions have been successfully executed on the OMEGA Laser System in the last decade. However, extracting sufficient understanding from these experiments to develop new designs or to identify or mitigate degradation sources remains challenging. Recently, a statistical modeling approach was developed to successfully design and predict improved implosion experiments on OMEGA. Here, we show that one-dimensional simulations can be used to predict the outcomes of systematically perturbed three-dimensional simulations and that this statistical modeling approach can be used to identify or rule out physical mechanisms for some of the degradation sources observed on the OMEGA Laser System for direct-drive cryogenic inertial confinement fusion. In this instance, we investigate the fusion yield dependencies on the ion temperature asymmetries and laser beam size observed in experiments by comparing with trends in three-dimensional synthetic simulation databases. Using the statistical model on these systematically perturbed simulations, we find that the statistically inferred dependency on the measured ion temperature asymmetries is well explained by imposed ℓ =1 modes. However, we find that the dependency on the laser beam size is only dominated by the illumination non-uniformity for some extreme cases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Monolithic ceramic analysis using the SCARE program

The Structural Ceramics Analysis and Reliability Evaluation (SCARE) computer program calculates the fast fracture reliability of monolithic ceramic components. The code is a post-processor to the MSC/NASTRAN general purpose finite element program. The SCARE program automatically accepts the MSC/NASTRAN output necessary to compute reliability. This includes element stresses, temperatures, volumes, and areas. The SCARE program computes two-parameter Weibull strength distributions from input fracture data for both volume and surface flaws. The distributions can then be used to calculate the reliability of geometrically complex components subjected to multiaxial stress states. Several fracture criteria and flaw types are available for selection by the user, including out-of-plane crack extension theories. The theoretical basis for the reliability calculations was proposed by Batdorf. These models combine linear elastic fracture mechanics (LEFM) with Weibull statistics to provide a mechanistic failure criterion. Other fracture theories included in SCARE are the normal stress averaging technique and the principle of independent action. The objective of this presentation is to summarize these theories, including their limitations and advantages, and to provide a general description of the SCARE program, along with example problems.

Manderscheid, Jane M.↗

Linear canonical transformations of coherent and squeezed states in the Wigner phase space. III - Two-mode states

It is shown that the basic symmetry of two-mode squeezed states is governed by the group SP(4) in the Wigner phase space which is locally isomorphic to the (3 + 2)-dimensional Lorentz group. This symmetry, in the Schroedinger picture, appears as Dirac's two-oscillator representation of O(3,2). It is shown that the SU(2) and SU(1,1) interferometers exhibit the symmetry of this higher-dimensional Lorentz group. The mathematics of two-mode squeezed states is shown to be applicable to other branches of physics including thermally excited states in statistical mechanics and relativistic extended hadrons in the quark model.

Han, D.↗

Learning stochastic dynamics with statistics-informed neural network

We introduce a machine-learning framework named statistics-informed neural network (SINN) for learning stochastic dynamics from data. This new architecture was theoretically inspired by a universal approximation theorem for stochastic systems, which we introduce in this paper, and the projection-operator formalism for stochastic modeling. Here, we devise mechanisms for training the neural network model to reproduce the correct statistical behavior of a target stochastic process. Numerical simulation results demonstrate that a well-trained SINN can reliably approximate both Markovian and non-Markovian stochastic dynamics. We demonstrate the applicability of SINN to coarse-graining problems and the modeling of transition dynamics. Furthermore, we show that the obtained reduced-order model can be trained on temporally coarse-grained data and hence is well suited for rare-event simulations.

97 MATHEMATICS AND COMPUTING↗

Probabilistic Material Strength Degradation Model for Inconel 718 Components Subjected to High Temperature, Mechanical Fatigue, Creep and Thermal Fatigue Effects

This thesis presents the on-going development of methodology for a probabilistic material strength degradation model. The probabilistic model, in the form of a postulated randomized multifactor equation, provides for quantification of uncertainty in the lifetime material strength of aerospace propulsion system components subjected to a number of diverse random effects. This model is embodied in the computer program entitled PROMISS, which can include up to eighteen different effects. Presently, the model includes four effects that typically reduce lifetime strength: high temperature, mechanical fatigue, creep, and thermal fatigue. Statistical analysis was conducted on experimental Inconel 718 data obtained from the open literature. This analysis provided regression parameters for use as the model's empirical material constants, thus calibrating the model specifically for Inconel 718. Model calibration was carried out for four variables, namely, high temperature, mechanical fatigue, creep, and thermal fatigue. Methodology to estimate standard deviations of these material constants for input into the probabilistic material strength model was developed. Using the current version of PROMISS, entitled PROMISS93, a sensitivity study for the combined effects of mechanical fatigue, creep, and thermal fatigue was performed. Results, in the form of cumulative distribution functions, illustrated the sensitivity of lifetime strength to any current value of an effect. In addition, verification studies comparing a combination of mechanical fatigue and high temperature effects by model to the combination by experiment were conducted. Thus, for Inconel 718, the basic model assumption of independence between effects was evaluated. Results from this limited verification study strongly supported this assumption.

Bast, Callie Corinne Scheidt↗

Statistical mechanics of soft-boson phase transitions

The existence of structure on large (100 Mpc) scales, and limits to anisotropies in the cosmic microwave background radiation (CMBR), have imperiled models of structure formation based solely upon the standard cold dark matter scenario. Novel scenarios, which may be compatible with large scale structure and small CMBR anisotropies, invoke nonlinear fluctuations in the density appearing after recombination, accomplished via the use of late time phase transitions involving ultralow mass scalar bosons. Herein, the statistical mechanics are studied of such phase transitions in several models involving naturally ultralow mass pseudo-Nambu-Goldstone bosons (pNGB's). These models can exhibit several interesting effects at high temperature, which is believed to be the most general possibilities for pNGB's.

Gupta, Arun K.↗

Influence of the Convection Electric Field Models on Predicted Plasmapause Positions During Magnetic Storms

In the present work, we determine how three well documented models of the magnetospheric electric field, and two different mechanisms proposed for the formation of the plasmapause influence the radial distance, the shape and the evolution of the plasmapause during the geomagnetic storms of 28 October 2001 and of 17 April 2002. The convection electric field models considered are: Mcllwain's E51) electric field model, Volland-Stern's model and Weimer's statistical model compiled from low-Earth orbit satellite data. The mechanisms for the formation of the plasmapause to be tested are: (i) the MHD theory where the plasmapause should correspond to the last-closed- equipotential (LCE) or last-closed-streamline (LCS), if the E-field distribution is stationary or time-dependent respectively; (ii) the interchange mechanism where the plasmapause corresponds to streamlines tangent to a Zero-Parallel-Force surface where the field-aligned plasma distribution becomes convectively unstable during enhancements of the E-field intensity in the nightside local time sector. The results of the different time dependent simulations are compared with concomitant EUV observations when available. The plasmatails or plumes observed after both selected geomagnetic storms are predicted in all simulations and for all E-field models. However, their shapes are quite different depending on the E-field models and the mechanisms that are used. Despite the partial success of the simulations to reproduce plumes during magnetic storms and substorms, there remains a long way to go before the detailed structures observed in the EUV observations during periods of geomagnetic activity can be accounted for very precisely by the existing E-field models. Furthermore, it cannot be excluded that the mechanisms currently identified to explain the formation of "Carpenter's knee" during substorm events, will', have to be revised or complemented in the cases of geomagnetic storms.

Pierrard, V.↗

Rotor noise due to atmospheric turbulence ingestion. I - Fluid mechanics

In the present analytical procedure for the prediction of helicopter rotor noise generation due to the ingestion of atmospheric turbulence, different models for turbulence fluid mechanics and the ingestion process are combined. The mean flow and turbulence statistics associated with the atmospheric boundary layer are modeled with attention to the effects of atmospheric stability length, windspeed, and altitude. The turbulence field can be modeled as isotropic, locally stationary, and homogeneous. For large mean flow contraction ratios, accurate predictions of turbulence vorticity components at the rotor face requires the incorporation of the differential drift of fluid particles on adjacent streamlines.

Simonich, J. C.↗

Computation of conventional and alternative jet fuel sensitivity to lean blowout

Large Eddy Simulations (LES) are performed to compute the sensitivity of a conventional (A-2) and an alternate bio-jet (C-1) fuel to Lean Blowout (LBO). A realistic aviation gas turbine engine combustor configuration is considered. Reliable experimental LBO data and OH* chemiluminescence data for the conventional and alternate jet fuel in the combustor configuration have recently become available. The present work utilizes a highly automated, on-the-fly meshing strategy, along with adaptive mesh refinement, to demonstrate the feasibility of capturing the realistic combustion processes. A Lagrangian framework, with initial conditions specified using measurements of spray statistics, is used to model the fuel spray. Newly developed compact reaction mechanisms based on fuel surrogates are validated for the A-2 and the C-1 fuels. The compact reaction mechanisms are implemented using a detailed finite rate chemistry solver. Spray statistics computed by the present LES simulations compare well with available measurements at stable flame conditions near the lean blowout limit. The computed shape of the stable flame as represented by line integrated OH concentrations compares well with the experimental OH* chemiluminescence data. Lean blowout is reached by gradually decreasing the fuel flow rate in the computations, similar to that in the experiments. The results of the LES simulations effectively capture the fuel composition effects and estimate the sensitivity of the LBO limits to the fuel type. The computed trends in LBO limits agree within engineering accuracy with the experimental results for conventional and alternative aviation fuels. The methodology for predicting the fuel composition effects on the lean blowout limits in a fully resolved realistic, complex combustor is established for the first time.

Adaptive mesh refinement↗

Deep Koopman operators for causal discovery

Causal discovery aims to identify cause-effect mechanisms for better scientific understanding, explainable decision-making, and more accurate modeling. Standard statistical frameworks, such as Granger causality, lack the ability to quantify causal relationships in nonlinear dynamics due to the presence of complex feedback mechanisms, timescale mixing, and nonstationarity. Thus, applying these methods to study causal dynamics in real-world systems, such as the Earth, is a major challenge. Addressing this shortcoming, we leverage deep learning and a Koopman operator-theoretic formalism to present a class of causal discovery algorithms. Kausal uses deep Koopman operator methods to approximate nonlinear dynamics in a linearized vector space in which traditional causal inference methods such as Granger causality can be more easily applied. Our idealized experiments demonstrate Kausal’s superior ability in discovering and characterizing causal signals compared to existing deep learning and non-deep learning state-of-the-art approaches. Finally, the successful identification of major El Niño and La Niña events in observations showcases Kausal’s skill to handle real-world applications.

54 ENVIRONMENTAL SCIENCES↗