SEARCH · Search NASA

Results for “Green–Kubo equations”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

11 records

All sources NASA NTRS DOE OSTI

DOE OSTI2024

Site-Projected Thermal Conductivity: Application to Defects, Interfaces, and Homogeneously Disordered Materials

With the rapid advance of high-performance computing and electronic technologies, understanding thermal conductivity in materials has become increasingly important. This study presents a novel method: the site-projected thermal conductivity that quantitatively estimates the local (atomic) contribution to heat transport, leveraging the Green–Kubo thermal transport equations. The effectiveness of this approach on disordered and amorphous graphene, amorphous silicon, and grain boundaries in silicon–germanium alloys is demonstrated. Amorphous graphene reveals a percolation behavior for thermal transport. The results highlight the potential of the method to provide new insights into the thermal behavior of materials, offering a promising avenue for materials design and performance optimization.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Simplified Universal Equations for Ionic Conductivity and Transference Number

Nernst-Einstein equation can provide a reasonable estimate of the ionic conductivity of dilute solutions. For concentrated solutions, alternate methods such as Green–Kubo relations and Einstein relations are more suitable to account for ion-ion interactions. Such computations can be expensive for multicomponent systems. Simplified mathematical expressions like the Nernst-Einstein equation do not exist for concentrated multicomponent mixtures. Newman’s treatment of multicomponent concentrated solutions yields a conductivity relation in terms of species concentration and Onsager phenomenological coefficients. However, the estimation of these phenomenological coefficients is not straightforward. Here, mathematical formulations that relate the phenomenological coefficients with the friction coefficients are developed, leading to simplified, ready-to-use expressions of conductivity and transference numbers that can be used for a wide range of ionic mixtures. This approach involves spectral decomposition of the matrix of Onsager phenomenological coefficients. The general analytical expressions for conductivity and transference number are simplified for binary electrolytes, and numerical solutions are provided for ternary and quaternary mixtures with ion dissociation.

Electrochemistry↗

DOE OSTI2025

Foundations of magnetohydrodynamics

In this tutorial, a derivation of magnetohydrodynamics (MHD) valid beyond the usual ideal gas approximation is presented. Non-equilibrium thermodynamics is used to obtain conservation equations and linear constitutive relations. When coupled with Maxwell's equations, this provides closed fluid equations in terms of material properties of the plasma, described by the equation of state and transport coefficients. These properties are connected to microscopic dynamics using the Irving–Kirkwood procedure and Green–Kubo relations. Symmetry arguments and the Onsager–Casimir relations allow one to vastly simplify the number of independent coefficients. Importantly, expressions for current density, heat flux, and stress (conventionally Ohm's law, Fourier's law, and Newton's law) take different forms in systems with a non-ideal equation of state. The traditional form of the MHD equations, which is usually obtained from a Chapman–Enskog solution of the Boltzmann equation, corresponds to the ideal gas limit of the general equations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Transport phenomena in electrolyte solutions: Nonequilibrium thermodynamics and statistical mechanics

The theory of transport phenomena in multicomponent electrolyte solutions is presented here through the integration of continuum mechanics, electromagnetism, and nonequilibrium thermodynamics. The governing equations of irreversible thermodynamics, including balance laws, Maxwell's equations, internal entropy production, and linear laws relating the thermodynamic forces and fluxes, are derived. Green–Kubo relations for the transport coefficients connecting electrochemical potential gradients and diffusive fluxes are obtained in terms of the flux–flux time correlations. Furthermore, the relationship between the derived transport coefficients and those of the Stefan–Maxwell and infinitely dilute frameworks are presented, and the connection between the transport matrix and experimentally measurable quantities is described. To exemplify the application of the derived Green–Kubo relations in molecular simulations, the matrix of transport coefficients for lithium and chloride ions in dimethyl sulfoxide is computed using classical molecular dynamics and compared with experimental measurements.

42 ENGINEERING↗

DOE OSTI2021

Fluctuating hydrodynamics of chiral active fluids

Active materials are characterized by continuous injection of energy at the microscopic level and typically cannot be adequately described by equilibrium thermodynamics. Here we study a class of active fluids in which equilibrium-like properties emerge when fluctuating and activated degrees of freedom are statistically decoupled, such that their mutual information is negligible. We analyse three paradigmatic systems: chiral active fluids composed of spinning frictional particles that are free to translate, oscillating granular gases and active Brownian rollers. In all of these systems, a single effective temperature generated by activity parameterizes both the equation of state and the emergent Boltzmann statistics. The same effective temperature, renormalized by velocity correlations, relates viscosities to steady-state stress fluctuations via a Green–Kubo relation. To rationalize these observations, we develop a theory for the fluctuating hydrodynamics of these non-equilibrium fluids and validate it through large-scale molecular dynamics simulations. Our work sheds light on the microscopic origin of odd viscosities and stress fluctuations characteristic of parity-violating fluids, in which mirror symmetry and detailed balance are broken.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2024

Phonon modal analysis of thermal transport in ThO 2 with point defects using equilibrium molecular dynamics

Defects can significantly degrade the thermal conductivity of ThO 2 , an advanced nuclear fuel material as well as a surrogate for other fluorite-structured materials. Here, we investigate how point defects in ThO 2 impact phonon mode-resolved thermal transport. By incorporating phonon modes from lattice dynamics, we decompose the trajectory and heat flux to phonon normal mode space and extract key phonon properties, including phonon relaxation times and their contributions to thermal conductivity. We implement two methods. The first method is based on the Green Kubo formalism to resolve the contribution of each phonon mode to thermal conductivity. The second resolves the lifetime of individual phonon modes and the thermal conductivity is calculated using the Boltzmann transport equation within relaxation time approximation. Notably, a lower contribution of acoustic modes is revealed compared to perturbative approaches considering only three-phonon scattering processes. The effects of four types of point defects are evaluated. The strongest impact on a reduction in thermal conductivity is from Th interstitials, followed by Th vacancies. O interstitials/vacancies have a similar impact, albeit smaller than defects on the thorium sublattice. These observations are consistent with previous studies.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2026

Seamlessly joining length scales: From atomistic thermal graphs to anisotropic continuum conductivity

Thermal transport in complex solids is governed by local structure, defects, and anisotropy, yet most continuum models still rely on oversimplified and homogenized conductivities. Here, we bridge atomistic and continuum descriptions by building finite element (FE) models directly from the site-projected thermal conductivity (SPTC), an atomic-level decomposition of the Green–Kubo thermal conductivity. We introduce a toolkit, the “Simulator Collection for Atomic-to-Continuum Scales (SCACS)”, which uses a graph neural network to predict SPTC on large atomic structures, coarse-grains these fields into anisotropic conductivity tensors, and embeds them into the heat-flow FE equation with a customized, anisotropy-aware adaptive mesh refinement scheme. Applied to silicon nanostructures, the resulting FE models act as representative volume elements, reproduce bulk conductivities, and capture interfacial and defect-driven anisotropy while maintaining thermodynamic consistency. Additionally, SCACS predicts experimental conductance trends and fields. This work demonstrates a general route for transferring atomistic transport information into device-scale thermal simulations with physics-based approximations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Intermediate polaronic charge transport in organic crystals from a many-body first-principles approach

Abstract Charge transport in organic molecular crystals (OMCs) is conventionally categorized into two limiting regimes − band transport, characterized by weak electron-phonon (e-ph) interactions, and charge hopping due to localized polarons formed by strong e-ph interactions. However, between these two limiting cases there is a less well understood intermediate regime where polarons are present but transport does not occur via hopping. Here we show a many-body first-principles approach that can accurately predict the carrier mobility in this intermediate regime and shed light on its microscopic origin. Our approach combines a finite-temperature cumulant method to describe strong e-ph interactions with Green-Kubo transport calculations. We apply this parameter-free framework to naphthalene crystal, demonstrating electron mobility predictions within a factor of 1.5−2 of experiment between 100 and 300 K. Our analysis reveals the formation of a broad polaron satellite peak in the electron spectral function and the failure of the Boltzmann equation in the intermediate regime.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Time reversal symmetry breaking and odd viscosity in active fluids: Green–Kubo and NEMD results

Active fluids, which are driven at the microscale by non-conservative forces, are known to exhibit novel transport phenomena due to the breaking of time reversal symmetry. Recently, Epstein and Mandadapu [arXiv:1907.10041 (2019)] obtained Green-Kubo relations for the full set of viscous coefficients governing isotropic chiral active fluids, including the so-called odd viscosity, invoking Onsager's regression hypothesis for the decay of fluctuations in active non-equilibrium steady states. In this Communication, we test these Green-Kubo relations using molecular dynamics simulations of a canonical model system consisting of actively torqued dumbbells. We find the resulting odd and shear viscosity values from the Green-Kubo relations to be in good agreement with values measured independently through non-equilibrium molecular dynamics flow simulations. This provides a test of the Green-Kubo relations and lends support to the application of the Onsager regression hypothesis in relation to viscous behaviors of active matter systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Atomistic simulations of the thermal conductivity of liquids

We present a method based on sinusoidal approach to equilibrium molecular dynamics (SAEMD) to compute the thermal conductivity of liquids Similar to nonequilibrium molecular dynamics, and unlike equilibrium simulations based on the Green-Kubo formalism, the method only requires the calculation of forces and total energies. The evaluation of heat fluxes and energy densities is not necessary, thus offering the promise of efficiently implementing first principles simulations based on density functional theory or deep molecular dynamics. Our approach is a generalization of SAEMD for solids, where the thermal conductivity is computed in the steady state, instead of a transient regime, thus properly taking into account diffusive terms in the heat equation. We present results for liquid water at ambient conditions and under pressure and discuss simulation requirements to obtain converged values of the thermal conductivity as a function of size and simulation time.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Predicted viscosity of liquid HMX up to 40 GPa

Viscous flow serves as a significant heating mechanism during the formation of hot spots, but the shear viscosity which determines this response is poorly characterized for most high explosives. Most recently, a model was proposed for the shear viscosity of liquid HMX (1,3,5,7-tetranitro-1,3,5,7-tetrazocane) that was fit to pressures reaching 5 GPa, but this work uncovered uncertainties in the viscosity at 0 GPa and remains untested at higher pressures. We use molecular dynamics (MD) simulations and the Green-Kubo formalism to predict the temperature- and pressure-dependent shear viscosity of HMX over the pressure interval 0 GPa≤P≤40 GPa. Reassessment of the viscosity at 0 GPa rules out several potential explanations for discrepancies between earlier reports; we attribute these differences to details of MD trajectory integration impacting molecular flexibility. The shear viscosity of HMX exhibits an Arrhenius temperature dependence at each pressure considered, with exponential prefactor and activation energy terms that are also strong functions of pressure. An analytic form for the viscosity is developed based on an extension of the well-known Andrade equation that simultaneously captures the temperature and pressure dependencies in the MD data up to 40 GPa. Comparison against a recently developed model for the viscosity of liquid RDX (1,3,5-trinitro-1,3,5-triazinane) shows that both materials exhibit similar functional dependencies with the viscosity of HMX being higher by roughly an order of magnitude at a given temperature-pressure state.

36 MATERIALS SCIENCE↗