Equation of state and the Hugoniot of laser shock-compressed deuterium: Demonstration of a basis-function-free method for quantum calculations
Bibliographic record
Abstract
In most density functionals the energy is a functional of the electron density $n(\stackrel{\ensuremath{\rightarrow}}{r})$ and a function of the nuclear positions ${R}_{i}.$ We consider, a functional of both$n(\stackrel{\ensuremath{\rightarrow}}{r})$ and the nuclear density $\ensuremath{\rho}(\stackrel{\ensuremath{\rightarrow}}{r})=\ensuremath{\sum}\ensuremath{\delta}(\stackrel{\ensuremath{\rightarrow}}{r}\ensuremath{-}{R}_{i}).$ In reducing the two Kohn--Sham equations, a classical mapping valid for interacting electrons is invoked. The exchange-correlation is nonlocal and free of self-interaction errors. As a challenging application, we calculate the equation of state and the shock Hugoniot of deuterium relevant to topical shock experiments. The calculated Hugoniot is quite close to the SESAME and path-integral Monte Carlo Hugoniots. We also treat the nonequilibrium case, which is extremely difficult for standard methods. Here the ${\mathrm{D}}^{+}$ are assumed to be hotter than the electrons, and lead to the soft Hugoniots similar to those seen in the laser-shock data. The softening arises from hot ${\mathrm{D}}^{+}--e$ pairs occurring close to the zero of the electron chemical potential.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".