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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.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

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↗
DOE OSTI2024

Statistical mechanics and pressure of composite multimoded weakly nonlinear optical systems

Statistical mechanics can provide a versatile theoretical framework for investigating the collective dynamics of weakly nonlinear-wave settings that can be utterly complex to describe otherwise. In optics, composite systems arise due to interactions between different frequencies and polarizations. The purpose of this work is to develop a thermodynamic theory that takes into account the synergistic action of multiple components. We find that the type of the nonlinearity involved can have important implications in the thermalization process and, hence, can lead to different thermal equilibrium conditions. Importantly, we derive closed-form expressions for the actual optomechanical pressure that is exerted on the system. In particular, the total optomechanical pressure is the sum of the partial pressures due to each component. Our results can be applied to a variety of weakly nonlinear optical settings such as multimode fibers, bulk waveguides, photonic lattices, and coupled microresonators. We present two specific examples, where two colors interact in a one-waveguide array with either a cubic or quadratic nonlinearity.

Efremidis, Nikolaos K. (ORCID:0000000298300268)↗
DOE OSTI2014

Statistical mechanical models for dissociative adsorption of O{sub 2} on metal(100) surfaces with blocking, steering, and funneling

We develop statistical mechanical models amenable to analytic treatment for the dissociative adsorption of O{sub 2} at hollow sites on fcc(100) metal surfaces. The models incorporate exclusion of nearest-neighbor pairs of adsorbed O. However, corresponding simple site-blocking models, where adsorption requires a large ensemble of available sites, exhibit an anomalously fast initial decrease in sticking. Thus, in addition to blocking, our models also incorporate more facile adsorption via orientational steering and funneling dynamics (features supported by ab initio Molecular Dynamics studies). Behavior for equilibrated adlayers is distinct from those with finite adspecies mobility. We focus on the low-temperature limited-mobility regime where analysis of the associated master equations readily produces exact results for both short- and long-time behavior. Kinetic Monte Carlo simulation is also utilized to provide a more complete picture of behavior. These models capture both the initial decrease and the saturation of the experimentally observed sticking versus coverage, as well as features of non-equilibrium adlayer ordering as assessed by surface-sensitive diffraction.

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

Catalytic conversion reactions in nanoporous systems with concentration-dependent selectivity: Statistical mechanical modeling

Statistical mechanical modeling is developed to describe a catalytic conversion reaction A → B c or B t with concentration-dependent selectivity of the products, B c or B t , where reaction occurs inside catalytic particles traversed by narrow linear nanopores. The associated restricted diffusive transport, which in the extreme case is described by single-file diffusion, naturally induces strong concentration gradients. Hence, by comparing kinetic Monte Carlo simulation results with analytic treatments, selectivity is shown to be impacted by strong spatial correlations induced by restricted diffusivity in the presence of reaction and also by a subtle clustering of reactants, A.

36 MATERIALS SCIENCE↗
DOE OSTI2014

Random paths and current fluctuations in nonequilibrium statistical mechanics

An overview is given of recent advances in nonequilibrium statistical mechanics about the statistics of random paths and current fluctuations. Although statistics is carried out in space for equilibrium statistical mechanics, statistics is considered in time or spacetime for nonequilibrium systems. In this approach, relationships have been established between nonequilibrium properties such as the transport coefficients, the thermodynamic entropy production, or the affinities, and quantities characterizing the microscopic Hamiltonian dynamics and the chaos or fluctuations it may generate. This overview presents results for classical systems in the escape-rate formalism, stochastic processes, and open quantum systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2006

Exploring the Connection Between Sampling Problems in Bayesian Inference and Statistical Mechanics

The Bayesian and statistical mechanical communities often share the same objective in their work - estimating and integrating probability distribution functions (pdfs) describing stochastic systems, models or processes. Frequently, these pdfs are complex functions of random variables exhibiting multiple, well separated local minima. Conventional strategies for sampling such pdfs are inefficient, sometimes leading to an apparent non-ergodic behavior. Several recently developed techniques for handling this problem have been successfully applied in statistical mechanics. In the multicanonical and Wang-Landau Monte Carlo (MC) methods, the correct pdfs are recovered from uniform sampling of the parameter space by iteratively establishing proper weighting factors connecting these distributions. Trivial generalizations allow for sampling from any chosen pdf. The closely related transition matrix method relies on estimating transition probabilities between different states. All these methods proved to generate estimates of pdfs with high statistical accuracy. In another MC technique, parallel tempering, several random walks, each corresponding to a different value of a parameter (e.g. "temperature"), are generated and occasionally exchanged using the Metropolis criterion. This method can be considered as a statistically correct version of simulated annealing. An alternative approach is to represent the set of independent variables as a Hamiltonian system. Considerab!e progress has been made in understanding how to ensure that the system obeys the equipartition theorem or, equivalently, that coupling between the variables is correctly described. Then a host of techniques developed for dynamical systems can be used. Among them, probably the most powerful is the Adaptive Biasing Force method, in which thermodynamic integration and biased sampling are combined to yield very efficient estimates of pdfs. The third class of methods deals with transitions between states described by rate constants. These problems are isomorphic with chemical kinetics problems. Recently, several efficient techniques for this purpose have been developed based on the approach originally proposed by Gillespie. Although the utility of the techniques mentioned above for Bayesian problems has not been determined, further research along these lines is warranted

Pohorille, Andrew↗
DOE OSTI2025

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↗
DOE OSTI2025

Lectures on statistical mechanics

Presented here is a transcription of the lecture notes from Professor Allan N. Kaufman’s graduate statistical mechanics course Physics 212A and 212B at the University of California Berkeley from the 1972–1973 academic year. 212A addressed equilibrium statistical mechanics with topics: fundamentals (micro-canonical and sub-canonical ensembles, adiabatic law and action conservation, fluctuations, pressure, and virial theorem), classical fluids and other systems (equation of state, deviations from ideality, virial coefficients and van der Waals potential, canonical ensemble and partition function, quasistatic evolution, grand-canonical ensemble and partition function, chemical potential, simple model of a phase transition, quantum virial expansion, numerical simulation of equations of state, and phase transition), chemical equilibrium (systems with multiple species and chemical reactions, law of mass action, Saha equation, chemical equilibrium including ionization and excited states), and long-range interactions (including Coulomb, dipole, and gravitational interactions, Debye–Hückel theory, and shielding). 212B addressed nonequilibrium statistical mechanics with topics: fundamentals (definitions: realizations, moments, characteristic function, and discrete variables), Brownian motion (Langevin equation, fluctuation–dissipation theorem, spatial diffusion, Boltzmann’s H-theorem), Liouville and Klimontovich equations, Landau equation (derivation, elaboration, and H-theorem, and irreversibility), Markov processes and Fokker–Planck equation (derivations of the Fokker–Planck equation and a master equation), linear response and transport theory (linear Boltzmann equation, linear response theory of Kubo and Mori, relation of entropy production to electrical conductivity, transport relations and coefficients, normal mode solutions of the transport equations, sketch of a generalized Langevin equation method for transport theory), and an introduction to nonequilibrium quantum statistical mechanics.

plasma dynamics↗
DOE OSTI2018

Edwards statistical mechanics for jammed granular matter

In 1989, Sir Sam Edwards made the visionary proposition to treat jammed granular materials using a volume ensemble of equiprobable jammed states in analogy to thermal equilibrium statistical mechanics, despite their inherent athermal features. Since then, the statistical mechanics approach for jammed matter—one of the very few generalizations of Gibbs-Boltzmann statistical mechanics to out-of-equilibrium matter—has garnered an extraordinary amount of attention by both theorists and experimentalists. Its importance stems from the fact that jammed states of matter are ubiquitous in nature appearing in a broad range of granular and soft materials such as colloids, emulsions, glasses, and biomatter. Indeed, despite being one of the simplest states of matter—primarily governed by the steric interactions between the constitutive particles—a theoretical understanding based on first principles has proved exceedingly challenging. Here a systematic approach to jammed matter based on the Edwards statistical mechanical ensemble is reviewed. The construction of microcanonical and canonical ensembles based on the volume function, which replaces the Hamiltonian in jammed systems, is discussed. The importance of approximation schemes at various levels is emphasized leading to quantitative predictions for ensemble averaged quantities such as packing fractions and contact force distributions. An overview of the phenomenology of jammed states and experiments, simulations, and theoretical models scrutinizing the strong assumptions underlying Edwards approach is given including recent results suggesting the validity of Edwards ergodic hypothesis for jammed states. A theoretical framework for packings whose constitutive particles range from spherical to nonspherical shapes such as dimers, polymers, ellipsoids, spherocylinders or tetrahedra, hard and soft, frictional, frictionless and adhesive, monodisperse, and polydisperse particles in any dimensions is discussed providing insight into a unifying phase diagram for all jammed matter. Furthermore, the connection between the Edwards ensemble of metastable jammed states and metastability in spin glasses is established. This highlights the fact that the packing problem can be understood as a constraint satisfaction problem for excluded volume and force and torque balance leading to a unifying framework between the Edwards ensemble of equiprobable jammed states and out-of-equilibrium spin glasses.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

A reductionist perspective on quantum statistical mechanics: Coarse-graining of path integrals

Computational modeling of the condensed phase based on classical statistical mechanics has been rapidly developing over the last few decades and has yielded important information on various systems containing up to millions of atoms. However, if a system of interest contains important quantum effects, well-developed classical techniques cannot be used. One way of treating finite temperature quantum systems at equilibrium has been based on Feynman’s imaginary time path integral approach and the ensuing quantum-classical isomorphism. This isomorphism is exact only in the limit of infinitely many classical quasiparticles representing each physical quantum particle. In this work, we present a reductionist perspective on this problem based on the emerging methodology of coarse-graining. This perspective allows for the representations of one quantum particle with only two classical-like quasiparticles and their conjugate momenta. One of these coupled quasiparticles is the centroid particle of the quantum path integral quasiparticle distribution. Only this quasiparticle feels the potential energy function. The other quasiparticle directly provides the observable averages of quantum mechanical operators. The theory offers a simplified perspective on quantum statistical mechanics, revealing its most reductionist connection to classical statistical physics. By doing so, it can facilitate a simpler representation of certain quantum effects in complex molecular environments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1990

Statistical mechanics models for motion and force planning

The models of statistical mechanics provide an alternative to the methods of classical mechanics more traditionally used in robotics. They have a potential to: improve analysis of object collisions; handle kinematic and dynamic contact interactions within the same frmework; and reduce the need for perfect deterministic world model information. The statistical mechanics models characterize the state of the system as a probability density function (p.d.f.) whose time evolution is governed by a partial differential equation subject to boundary and initial conditions. The boundary conditions when rigid objects collide reflect the conservation of momentum. The models are being developed to embedd in remote semi-autonomous systems with a need to reason and interact with a multiobject environment.

Rodriguez, G.↗