Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “statistical mechanics models”

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 127 records · Page 7

Quantum mechanical closure of partial differential equations with symmetries

We develop a statistical framework for the dynamical closure of spatiotemporal dynamics governed by partial differential equations. Employing the mathematical framework of quantum mechanics to embed the original classical dynamics into a quantum mechanical representation, we use the space of quantum density operators to model the unresolved degrees of freedom of the original dynamics in a statistical sense, and the framework of quantum measurement to predict their contributions to the resolved dynamics. The embedded dynamics is discretized by a positivity preserving process, leading to a compressed representation that is invariant under the dynamical symmetries of the resolved dynamics. We present a data based formulation of the closure scheme and apply it to a closure problem for the shallow water equations. The numerical results demonstrate that our closure model can accurately predict the main features of the true dynamics, including for out of sample initial conditions.

Delay embedding↗

A Causal Approach to Model Validation and Calibration

This poster presents a novel method for validation and verification that focuses on identifying causal relationships between data elements, moving beyond traditional statistical and machine learning approaches. These methods employ causal discovery techniques to reveal the underlying mechanisms of data generation. The research utilizes structural causal models and directed acyclic graphs to depict causal relationships. This approach assists in achieving alignment between simulation models and reality.

97 MATHEMATICS AND COMPUTING↗

When do short-range atomistic machine-learning models fall short?

In this work, we explore the role of long-range interactions in atomistic machine-learning models by analyzing the effects on fitting accuracy, isolated cluster properties, and bulk thermodynamic properties. Such models have become increasingly popular in molecular simulations given their ability to learn highly complex and multi-dimensional interactions within a local environment; however, many of them fundamentally lack a description of explicit long-range interactions. In order to provide a well-defined benchmark system with precisely known pairwise interactions, we chose as the reference model a flexible version of the Extended Simple Point Charge (SPC/E) water model. Our analysis shows that while local representations are sufficient for predictions of the condensed liquid phase, the short-range nature of machine-learning models falls short in representing cluster and vapor phase properties. These findings provide an improved understanding of the role of long-range interactions in machine learning models and the regimes where they are necessary.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Search for new physics in high-mass diphoton events from proton-proton collisions at $ \sqrt{\textrm{s}} $ = 13 TeV

Results are presented from a search for new physics in high-mass diphoton events from proton-proton collisions at $ \sqrt{s} $ = 13 TeV. The data set was collected in 2016–2018 with the CMS detector at the LHC and corresponds to an integrated luminosity of 138 fb$^{−1}$. Events with a diphoton invariant mass greater than 500 GeV are considered. Two different techniques are used to predict the standard model backgrounds: parametric fits to the smoothly-falling background and a first-principles calculation of the standard model diphoton spectrum at next-to-next-to-leading order in perturbative quantum chromodynamics calculations. The first technique is sensitive to resonant excesses while the second technique can identify broad differences in the invariant mass shape. The data are used to constrain the production of heavy Higgs bosons, Randall-Sundrum gravitons, the large extra dimensions model of Arkani-Hamed, Dimopoulos, and Dvali (ADD), and the continuum clockwork mechanism. No statistically significant excess is observed. The present results are the strongest limits to date on ADD extra dimensions and RS gravitons with a coupling parameter greater than 0.1.[graphic not available: see fulltext]

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Strong Hilbert space fragmentation and fractons from subsystem and higher-form symmetries

Here, we introduce a route to Hilbert space fragmentation in high dimensions leveraging the group-word formalism. We show that taking strongly fragmented models in one dimension and “lifting” to higher dimensions using subsystem symmetries can yield strongly fragmented dynamics in higher dimensions, with subdimensional (e.g., lineonic) excitations. This provides a route to higher-dimensional strong fragmentation, and also a route to fractonic behavior. Meanwhile, lifting one-dimensional fragmented models to higher dimensions using higher-form symmetries yields models with topologically robust fragmentation. In three or more spatial dimensions, one can also “mix and match” subsystem and higher-form symmetries, leading to canonical fracton models such as X cube. We speculate that this approach could also yield a route to non-Abelian fractons. These constructions unify a number of phenomena that have been discussed in the literature, as well as furnishing models with unique properties.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Parameter-free prediction of phase transition in PbTiO 3 through combination of quantum mechanics and statistical mechanics

Thermodynamics of ferroelectric materials and their ferroelectric to paraelectric (FE-PE) transitions is commonly described by the phenomenological Landau theory and more recently by effective Hamiltonian and various potentials, all with model parameters fitted to experimental or theoretical data. Here, in this work, we show that the zentropy theory, which considers the total entropy of a system as a weighted sum of entropies of configurations that the system may experience and the statistical entropy among the configurations, can predict the FE-PE transition without fitting parameters. For PbTiO 3 , the configurations are identified as the FE configurations with 90- or 180° domain walls in addition to the ground state FE configuration without domain wall. With the domain wall energies predicted from first-principles based on density functional theory in the literature as the only inputs, the FE-PE transition for PbTiO 3 is predicted showing remarkable agreement with experiments, unveiling the microscopic fundamentals of the transition.

36 MATERIALS SCIENCE↗

Enhanced accuracy through ensembling of randomly initialized auto-regressive models for dynamical systems

Computational mechanics simulations using traditional finite element methods (FEM) require prohibitively expensive computational resources for real-time engineering applications, design optimization, and digital twin implementations. While machine learning (ML) surrogate models offer significant computational speedups, autoregressive ML models for time-dependent mechanical systems suffer from error accumulation that compromises long-term prediction reliability - a critical concern for engineering applications where accuracy over extended time horizons is essential for safety and performance assessments. Here, we propose a deep ensemble framework specifically designed to address this challenge in computational mechanics applications, where multiple ML surrogate models with random weight initializations are trained in parallel and their predictions aggregated during inference. This approach leverages statistical diversity to maximize information gain from a fixed set of training data and to mitigate error propagation, while maintaining the computational efficiency that makes ML surrogates attractive for engineering practice. We validate the framework on three representative problems spanning critical areas of computational mechanics: stress field evolution in heterogeneous microstructures under complex loading (relevant to advanced materials design and composite analysis), planetary-scale shallow water dynamics (applicable to environmental and geotechnical engineering), and Gray-Scott reaction-diffusion systems (relevant to mass transport and chemical process engineering). Across all test cases, the ensemble approach demonstrates consistent error reduction of 15-33% compared to individual models. The codes for this work are available on GitHub (https://github.com/Graham-Brady-Research-Group/AutoregressiveEnsemble_SpatioTemporal_Evolution).

autoregressive prediction↗

Mean-field control for efficient mixing of energy loads

In this work, we pose an engineering challenge of controlling an ensemble of energy devices via coordinated, implementation-light, and randomized on/off switching as a problem in nonequilibrium statistical mechanics. We show that mean-field control with nonlinear feedback on the cumulative consumption, assumed available to the aggregator via direct physical measurements of the energy flow, allows the ensemble to recover from its use in the demand response regime, i.e., transition to a statistical steady state, significantly faster than in the case of the fixed feedback. Moreover when the nonlinearity is sufficiently strong, one observes the phenomenon of “super-relaxation,” where the total instantaneous energy consumption of the ensemble transitions to the steady state much faster than the underlying probability distribution of the devices over their state space, while also leaving almost no devices outside of the comfort zone.

25 ENERGY STORAGE↗

AN ESTIMATE OF SPENT NUCLEAR FUEL MECHANICAL LOADS IN THE GENERAL 30 CM PACKAGE DROP SCENARIO

The US Department of Energy Spent Fuel and Waste Science and Technology (SFWST) program is performing research to determine the mechanical loading conditions applied to spent nuclear fuel (SNF) during normal conditions of transport to inform mechanical tests of SNF and close an important knowledge gap related to the practical disposition of SNF in the US. Researchers at Pacific Northwest National Laboratory (PNNL) have completed an extensive finite element study to characterize and estimate the potential mechanical loads on SNF during a hypothetical 30 cm drop of an SNF transportation package. This modeling study is validated with test data collected by the SFWST program during a physical test campaign that included one-third scale package drop tests and full-scale single fuel assembly drop tests. The test campaign was led by Sandia National Laboratories (SNL) and included international collaboration with Equipos Nucleares S.A, S.M.E (ENSA) and Bundesanstalt für Materialforschung und -prüfung (BAM). The key contribution of the modeling study is to go beyond the limitations of the limited number of physical tests to estimate the impact response to variations in impact angle, initial gap conditions, fuel assembly design, burnup and other parameters that affect the mechanical loads. The methodology of this study included a classic parametric study to calculate the impact response of highly detailed fuel assemblies over many combinations of parameters. Models of a 17x17 pressurized water reactor fuel assembly and a generic 10x10 boiling water reactor fuel assembly were both used in this study to cover the major fuel assembly types in the US inventory. Over 2,000 impact responses were calculated. The results of the parametric study were evaluated using traditional methods and basic statistics. The results were also used to construct a damage model using multiple nonlinear regression techniques to predict the mechanical loads over the full range of all input parameters. The damage model was found to work very well for all impact angle cases where the cask came to rest on its side. It was concluded that end drop cases where the cask remained vertical (instead of tipping over onto its side) were not sufficiently characterized by the current set of parametric study cases to include in the damage model, but it was not a priority to fully investigate that range because the highest mechanical loads were observed in the broader range of side impact cases. This modeling work provides sufficient insight into the mechanical loads on SNF during a hypothetical 30 cm package drop that, when considered along with the physical test data collected by the SNL-led team, the SFSWT program can consider the knowledge gap closed.

Klymyshyn, Nicholas A.↗

Separation of Radionuclides from a Rare Earth-Containing Solution by Zeolite Adsorption

The increasing industrial demand for rare earths requires new or alternative sources to be found. Within this context, there have been studies validating the technical feasibility of coal and coal byproducts as alternative sources for rare earth elements. Nonetheless, radioactive materials, such as thorium and uranium, are frequently seen in the rare earths’ mineralization, and causes environmental and health concerns. Consequently, there exists an urgent need to remove these radionuclides in order to produce high purity rare earths to diversify the supply chain, as well as maintain an environmentally-favorable extraction process for the surroundings. In this study, an experimental design was generated to examine the effect of zeolite particle size, feed solution pH, zeolite amount, and contact time of solid and aqueous phases on the removal of thorium and uranium from the solution. The best separation performance was achieved using 2.50 g of 12-µm zeolite sample at a pH value of 3 with a contact time of 2 h. Under these conditions, the adsorption recovery of rare earths, thorium, and uranium into the solid phase was found to be 20.43 wt%, 99.20 wt%, and 89.60 wt%, respectively. The Freundlich adsorption isotherm was determined to be the best-fit model, and the adsorption mechanism of rare earths and thorium was identified as multilayer physisorption. Further, the separation efficiency was assessed using the response surface methodology based on the development of a statistically significant model.

58 GEOSCIENCES↗

Multiscale Modeling Meets Machine Learning: What Can We Learn?

Machine learning is increasingly recognized as a promising technology in the biological, biomedical, and behavioral sciences. There can be no argument that this technique is incredibly successful in image recognition with immediate applications in diagnostics including electrophysiology, radiology, or pathology, where we have access to massive amounts of annotated data. However, machine learning often performs poorly in prognosis, especially when dealing with sparse data. This is a field where classical physics-based simulation seems to remain irreplaceable. In this review, we identify areas in the biomedical sciences where machine learning and multiscale modeling can mutually benefit from one another: Machine learning can integrate physics-based knowledge in the form of governing equations, boundary conditions, or constraints to manage ill-posted problems and robustly handle sparse and noisy data; multiscale modeling can integrate machine learn- ing to create surrogate models, identify system dynamics and parameters, analyze sensitivities, and quantify uncertainty to bridge the scales and understand the emergence of function. With a view towards applications in the life sciences, we discuss the state of the art of combining machine learning and multiscale modeling, identify applications and opportunities, raise open questions, and address potential challenges and limitations. We anticipate that it will stimulate discussion within the community of computational mechanics and reach out to other disciplines including mathematics, statistics, computer science, artificial intelligence, biomedicine, systems biology, and precision medicine to join forces towards creating robust and efficient models for biological systems.

machine learning, multiscale modeling, physics-bas↗

PaleoSTeHM v1.0: a modern, scalable spatiotemporal hierarchical modeling framework for paleo-environmental data

Abstract. Geological records of past environmental change provide crucial insights into long-term climate variability, trends, non-stationarity, and nonlinear feedback mechanisms. However, reconstructing spatiotemporal fields from these records is statistically challenging due to their sparse, indirect, and noisy nature. Here, we present PaleoSTeHM, a scalable and modern framework for spatiotemporal hierarchical modeling of paleo-environmental data. This framework enables the implementation of flexible statistical models that rigorously quantify spatial and temporal variability from geological data while clearly distinguishing measurement and inferential uncertainty from process variability. We illustrate its application by reconstructing temporal and spatiotemporal paleo-sea-level changes across multiple locations. Using various modeling and analysis choices, PaleoSTeHM demonstrates the impact of different methods on inference results and computational efficiency. Our results highlight the critical role of model selection in addressing specific paleo-environmental questions, showcasing the PaleoSTeHM framework's potential to enhance the robustness and transparency of paleo-environmental reconstructions.

58 GEOSCIENCES↗

Bayesian prior construction for uncertainty quantification in first-principles statistical mechanics

First-principles statistical mechanics enables the prediction of thermodynamic and kinetic properties of materials, but is computationally expensive. Many approaches require surrogate models to calculate energies within Monte Carlo or molecular dynamics simulations. Inexpensive surrogates such as cluster expansions enable otherwise intractable calculations by interpolating data from higher accuracy methods, such as Density Functional Theory (DFT). Surrogate models introduce uncertainty into downstream calculations, in addition to any uncertainty inherent to DFT calculations. Bayesian frameworks address this by quantifying uncertainty and incorporating expert knowledge through priors. However, constructing effective priors remains challenging. This work introduces and describes practical strategies for building Bayesian cluster expansions, focusing on basis truncation, hyperparameter selection, and ground state replication. We analyze multiple basis truncation schemes, compare cross-validation to the evidence-approximation for hyperparameter optimization, and provide methods to find and enforce ground-state-preserving models through priors. Additionally, we compare the uncertainties between different approximations to DFT (LDA, PBE, SCAN) against the uncertainty introduced with the use of cluster expansion surrogate models. These approaches are demonstrated on the BCC Li x Mg 1-x and Li x Al 1-x alloys, which are both of interest for solid-state Li batteries. Our results provide guidelines for constructing and utilizing Bayesian cluster expansions, thereby improving the transparency of materials modeling. Furthermore, the approaches and insights developed in this work can be transferred to a wide range of cluster expansion surrogate models, including the atomic cluster expansion and related machine-learned interatomic potential architectures.

Alloy theory↗

On the statistical theory of self-gravitating collisionless dark matter flow: Scale and redshift variation of velocity and density distributions

The statistics of velocity and density fields are crucial for cosmic structure formation and evolution. Here, this paper extends our previous work on the two-point second-order statistics for the velocity field [Phys. Fluids 35, 077105 (2023)] to one-point probability distributions for both density and velocity fields. The scale and redshift variation of density and velocity distributions are studied by a halo-based non-projection approach. First, all particles are divided into halo and out-of-halo particles so that the redshift variation can be studied via generalized kurtosis of distributions for halo and out-of-halo particles, respectively. Second, without projecting particle fields onto a structured grid, the scale variation is analyzed by identifying all particle pairs on different scales $r$. We demonstrate that: (i) Delaunay tessellation can be used to reconstruct the density field. The density correlation, spectrum, and dispersion functions were obtained, modeled, and compared with the N-body simulation; (ii) the velocity distributions are symmetric on both small and large scales and are non-symmetric with a negative skewness on intermediate scales due to the inverse energy cascade on small scales with a constant rate $\varepsilon_u$; (iii) On small scales, the even order moments of pairwise velocity $\Delta u_L$ follow a two-thirds law $\propto{(-\varepsilon_ur)}^{2/3}$, while the odd order moments follow a linear scaling $\langle(\Delta u_L)^{2n+1}\rangle=(2n+1)\langle(\Delta u_L)^{2n}\rangle\langle\Delta u_L\rangle\propto{r}$; (iv) The scale variation of the velocity distributions was studied for longitudinal velocities $u_L$ or $u_L^{'}$, pairwise velocity (velocity difference) $\Delta u_L$=$u_L^{'}$-$u_L$ and velocity sum $\Sigma u_L$=$u^{'}_L$+$u_L$. Fully developed velocity fields are never Gaussian on any scale, despite that they can initially be Gaussian; (v) On small scales, $u_L$ and $\Sigma u_L$ can be modeled by a $X$ distribution to maximize the entropy of the system. The distribution of $\Delta u_L$ can be different; (vi) On large scales, $\Delta u_L$ and $\Sigma u_L$ can be modeled by a logistic or a $X$ distribution, while $u_L$ has a different distribution; (vii) the redshift variation of the velocity distributions follows the evolution of the $X$ distribution involving a shape parameter $\alpha(z)$ decreasing with time.

79 ASTRONOMY AND ASTROPHYSICS↗

Computing Thermodynamic Properties of Fluids Augmented by Nanoconfinement: Application to Pressurized Methane

Nanoconfined fluids exhibit remarkably different thermodynamic behavior compared to the bulk phase. These confinement effects render predictions of thermodynamic quantities of nanoconfined fluids challenging. In particular, confinement creates a spatially varying density profile near the wall that is primarily responsible for adsorption and capillary condensation behavior. Significant fluctuations in thermodynamic quantities, inherent in such nanoscale systems, coupled to strong fluid–wall interactions give rise to this near-wall density profile. Empirical models have been proposed to explain and model these effects, yet no first-principles based formulation has been developed. We present a statistical mechanics framework that embeds such a coupling to describe the effect of the fluid–wall interaction in amplifying the near-wall density behavior for compressible gases at elevated pressures such as pressurized methane in confinement. We show that the proposed theory predicts accurately the adsorbed layer thickness as obtained with small-angle neutron scattering measurements. Furthermore, the predictions of density under confinement from the proposed theory are shown to be in excellent agreement with available experimental and atomistic simulations data for a range of temperatures for nanoconfined methane. While the framework is presented for evaluating the near-wall density, owing to its rigorous foundation in statistical mechanics, the proposed theory can also be generalized for predicting phase-transition and nonequilibrium transport of nanoconfined fluids.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Lieb-Robinson Light Cone for Power-Law Interactions

The Lieb-Robinson theorem states that information propagates with a finite velocity in quantum systems on a lattice with nearest-neighbor interactions. What are the speed limits on information propagation in quantum systems with power-law interactions, which decay as 1 / r α at distance r ? Here, we present a definitive answer to this question for all exponents α > 2 d and all spatial dimensions d . Schematically, information takes time at least r min { 1 , α - 2 d } to propagate a distance r . As recent state transfer protocols saturate this bound, our work closes a decades-long hunt for optimal Lieb-Robinson bounds on quantum information dynamics with power-law interactions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Dynamics of particle network in composite battery cathodes

We report that improving composite battery electrodes requires a delicate control of active materials and electrode formulation. The electrochemically active particles fulfill their role as energy exchange reservoirs through interacting with the surrounding conductive network. We formulate a network evolution model to interpret the regulation and equilibration between electrochemical activity and mechanical damage of these particles. Through statistical analysis of thousands of particles using x-ray phase contrast holotomography in a LiNi 0.8 Mn 0.1 Co 0.1 O 2 -based cathode, we found that the local network heterogeneity results in asynchronous activities in the early cycles, and subsequently the particle assemblies move toward a synchronous behavior. Our study pinpoints the chemomechanical behavior of individual particles and enables better designs of the conductive network to optimize the utility of all the particles during operation.

25 ENERGY STORAGE↗

Benchmarking Microscale Ductility Measurements (Final Report of the Project DE-NE0008799)

Conventional macroscale experimentation is generally considered to be straightforward with few limitations. Conversely, micro/nanoscale experimentation presents numerous challenges in loading device design, sample preparation and handling, as well as accurate understanding of grain size and local texture effects on recorded measurements. Despite these challenges, nanopillar compression, MEMs based micro-tension, and nanoindentation approaches have been able to provide fundamental contributions to the understanding of material behavior at small lengthscales. However, the overarching shortcoming of these micro/nanoscale experimentation approaches, is the inability to directly translate measurements evaluated at the nm and µm length scales (e.g., hardness) to macroscale tensile material behavior (i.e., elastic modulus, yield strength, and ductility). The objectives of the proposed study are, 1) to establish best practices for obtaining tensile microscale ductility measurements, and 2) to validate methodologies to for comparing microscale ductility measurements to macroscale ductility measurements. In order to achieve these objectives, a multi-lengthscale, multi-temperature testing protocol and simulation framework are executed first on copper as a model material to validate the following approach, and second on reactor grade Zircaloy-2. Experiments are conducted on specimens extracted from the same test piece to ensure nominally identical grain size and texture from specimens to specimen. Motivated by the need to isolate the contribution of size-effects on obtained mechanical property measurements, specimens are manufactured with thicknesses at the micro- (1-10 µm), meso- (10-100's µm), and macroscales (sub-sized ASTM E8). In-situ full-field deformation techniques (scanning electron microscopy (SEM) grid methods and optical DIC) are incorporated into testing at each specimen length-scale to capture plasticity localization and evolution. Experimental testing for all specimens is conducted at both room temperature and elevated temperatures to probe the role of thermal activation on plastic deformation accommodation processes. Simulation efforts focus on examining the mechanical behavior of microscale specimens using a finite element approach with explicitly resolved grain morphologies, and an embedded crystal plasticity model. The cost-efficient implementation method allows for the modeling of a statistically significant number of both real (i.e., digital twin) and generated microstructures to obtain an understanding of the interrelationships between specimen microstructure and geometric variables (grain size, texture, specimen geometry, etc.) on microscale mechanical behavior.

36 MATERIALS SCIENCE↗