Examining the effects of soil entrainment during nuclear cloud rise on fallout predictions using a multiscale atmospheric modeling framework.

Current operational models for nuclear cloud rise over land were developed and validated using observations from shallow-buried or surface detonations, where lofted soil quickly mixed with fission products from the detonation. These models poorly predict fallout from elevated detonations near the fallout-free height of burst (FFHOB), where interactions with the ground are limited and the mixing of fission products and lofted soil is incomplete. Fallout-free is a misnomer at this HOB, as fallout was observed in these cases, but was below the levels of concern, especially off-grounds of the nuclear test site. To correctly characterize and model fallout from detonations near the FFHOB, models must be developed which can capture the stratified nature of the particle and activity-size distributions within the cloud. Previously, it was shown that the Weather Research and Forecasting (WRF) model can accurately simulate nuclear cloud rise for airbursts with little to no ground interactions (Arthur et al., 2021). That work is expanded here by (1) using a radiation-hydrodynamics code to improve the fireball initialization in WRF, (2) further developing an aerosol package from WRF-Chem to simulate lofted soil, and (3) combining the WRF cloud rise simulations with the operational models used at the National Atmospheric Release Advisory Center (NARAC) for fallout modeling. Using this combination of codes, the Upshot-Knothole Grable detonation, which was just below the FFHOB, is simulated from seconds after detonation through cloud rise and fallout, and results are compared to historical test data. The results show improved prediction of dose rate and highlight the need to correctly characterize the entrainment of material into the cloud and the subsequent mixing of fission products with entrained material.

Analytic expressions for electron-ion temperature equilibration rates from the Lenard-Balescu equation.

In this work, we elucidate the mathematical structure of the integral that arises when computing the electron-ion temperature equilibration time for a homogeneous weakly coupled plasma from the Lenard-Balescu equation. With some minor approximations, we derive an analytic formula, requiring no input Coulomb logarithm, for the equilibration rate that is valid for moderate electron-ion temperature ratios and arbitrary electron degeneracy. For large temperature ratios, we derive the necessary correction to account for the coupled-mode effect, which can be evaluated very efficiently using ordinary Gaussian quadrature.

Molecular dynamics studies of electron-ion temperature equilibration in hydrogen plasmas within the coupled-mode regime.

We use classical molecular dynamics (MD) to study electron-ion temperature equilibration in two-component plasmas in regimes for which the presence of coupled collective modes has been predicted to substantively reduce the equilibration rate. Guided by previous kinetic theory work, we examine hydrogen plasmas at a density of n=10^{26}cm^{-3}, T_{i}=10^{5}K, and 10^{7}K

Density-functional calculations of transport properties in the nondegenerate limit and the role of electron-electron scattering.

We compute electrical and thermal conductivities of hydrogen plasmas in the nondegenerate regime using Kohn-Sham density functional theory (DFT) and an application of the Kubo-Greenwood response formula, and demonstrate that for thermal conductivity, the mean-field treatment of the electron-electron (e-e) interaction therein is insufficient to reproduce the weak-coupling limit obtained by plasma kinetic theories. An explicit e-e scattering correction to the DFT is posited by appealing to Matthiessen's Rule and the results of our computations of conductivities with the quantum Lenard-Balescu (QLB) equation. Further motivation of our correction is provided by an argument arising from the Zubarev quantum kinetic theory approach. Significant emphasis is placed on our efforts to produce properly converged results for plasma transport using Kohn-Sham DFT, so that an accurate assessment of the importance and efficacy of our e-e scattering corrections to the thermal conductivity can be made.

Percolation critical polynomial as a graph invariant.

Every lattice for which the bond percolation critical probability can be found exactly possesses a critical polynomial, with the root in [0,1] providing the threshold. Recent work has demonstrated that this polynomial may be generalized through a definition that can be applied on any periodic lattice. The polynomial depends on the lattice and on its decomposition into identical finite subgraphs, but once these are specified, the polynomial is essentially unique. On lattices for which the exact percolation threshold is unknown, the polynomials provide approximations for the critical probability with the estimates appearing to converge to the exact answer with increasing subgraph size. In this paper, I show how this generalized critical polynomial can be viewed as a graph invariant, similar to the Tutte polynomial. In particular, the critical polynomial is computed on a finite graph and may be found using the recursive deletion-contraction algorithm. This allows calculation on a computer, and I present such results for the kagome lattice using subgraphs of up to 36 bonds. For one of these, I find the prediction p(c)=0.52440572..., which differs from the numerical value, p(c)=0.52440503(5), by only 6.9×10(-7).

Molecular dynamics simulations and generalized Lenard-Balescu calculations of electron-ion temperature equilibration in plasmas.

We study the problem of electron-ion temperature equilibration in plasmas. We consider pure H at various densities and temperatures and Ar-doped H at temperatures high enough so that the Ar is fully ionized. Two theoretical approaches are used: classical molecular dynamics (MD) with statistical two-body potentials and a generalized Lenard-Balescu (GLB) theory capable of treating multicomponent weakly coupled plasmas. The GLB is used in two modes: (1) with the quantum dielectric response in the random-phase approximation (RPA) together with the pure Coulomb interaction and (2) with the classical (ℏ→0) dielectric response (both with and without local-field corrections) together with the statistical potentials. We find that the MD results are described very well by classical GLB including the statistical potentials and without local-field corrections (RPA only); worse agreement is found when static local-field effects are included, in contradiction to the classical pure-Coulomb case with like charges. The results of the various approaches are all in excellent agreement with pure-Coulomb quantum GLB when the temperature is high enough. In addition, we show that classical calculations with statistical potentials derived from the exact quantum two-body density matrix produce results in far better agreement with pure-Coulomb quantum GLB than classical calculations performed with older existing statistical potentials.

Critical surfaces for general bond percolation problems.

We present a general method for predicting bond percolation thresholds and critical surfaces for a broad class of two-dimensional periodic lattices, reproducing many known exact results and providing excellent approximations for several unsolved lattices. For the checkerboard and inhomogeneous bow-tie lattices, the method yields predictions that agree with numerical measurements to more than six figures, and are possibly exact.

Predictions of bond percolation thresholds for the kagomé and Archimedean (3, 12(2)) lattices.

Here we show how the recent exact determination of the bond percolation threshold for the martini lattice can be used to provide approximations to the unsolved kagomé and (3, 12(2)) lattices. We present two different methods: one which provides an approximation to the inhomogeneous kagomé and bond problems, and the other which gives estimates of for the homogeneous kagomé (0.524 408 8...) and (3, 12(2)) (0.740 421 2...) problems that, respectively, agree with numerical results to five and six significant figures.

Exact site percolation thresholds using a site-to-bond transformation and the star-triangle transformation.

I construct a two-dimensional lattice on which the inhomogeneous site percolation threshold is exactly calculable and use this result to find two more lattices on which the site thresholds can be determined. The primary lattice studied here, the "martini lattice," is a hexagonal lattice with every second site transformed into a triangle. The site threshold of this lattice is found to be 0.764826..., i.e., the solution to p4 - 3p3 + 1 = 0, while the others have (square root 5 - 1)/2 (the inverse of the golden ratio) and 1/square root 2. This last solution suggests a possible approach to establishing the bound for the hexagonal site threshold, pc < 1/square root 2. To derive these results, I solve a correlated bond problem on the hexagonal lattice by use of the star-triangle transformation and then, by a particular choice of correlations derived from a site-to-bond transformation, solve the site problem on the martini lattice.