Applications often require a fast, single-threaded search algorithm over sorted data, typical in table-lookup operations. We explore various search algorithms for a large number of search candidates over a relatively small array of logarithmically distributed sorted data. These include an innovative hash-based search that takes advantage of floating point representation to bin data by the exponent. Algorithms that can be optimized to take advantage of SIMD vector instructions are of particular interest. We then conduct a case study applying our results and analyzing algorithmic performance with the EOSPAC package. EOSPAC is a table lookup library for manipulation and interpolation of SESAME equation-of-state data. Our investigation results in a couple of algorithms with better performance with a best case 8x speedup over the original EOSPAC Hunt-and-Locate implementation. Our techniques are generalizable to other instances of search algorithms seeking to get a performance boost from vectorization.

(for Mie– Gr¨uneisen–Guggenheim–Barnes). Substance–specific parameters are obtained by fitting the low–density energy to data from the Sesame4 library; fitting the zero–temperature pressure to the Sesame cold curve; and fitting the saturation curve and latent heat to laboratory data,5 if available. When suitable coexistence data, or Sesame data, are not available, then we apply the Principle of Corresponding States.2 Thus MGGB can be thought of as a numerical recipe for rendering the tabular Sesame EOS data in an analytic form that includes a proper coexistence region, and which permits the accurate calculation of derivatives associated with compressibility, expansivity, Joule coefficient, and specific heat, all of which are required for multifield applications. 1

The Cross-Cutting Capabilities Project (XCAP) has significant interest in collecting and implementing a common set of libraries to be used across the various production hydro-codes at LANL. A common set of libraries will help facilitate comparisons between codes. In addition to minimizing variables for comparisons and physics validation, efforts toward optimization and porting of packages for future architectures will be more efficient. As part of this push Singularity is being considered as an inclusive materials interface library. One crucial part of this library is the importing, inverting, and interpolation of equation of state (EOS) data. Currently the Lagrangian Applications Project (LAP) and Safety Applications Project (SAP) are using EOSPAC6 for delivery EOS data. The Eulerian Applications Project (EAP) has historically used TEOS and more recently an implementation of Singularly via a package called Spiner for EOS interpolation. Singularity currently has the option of using several analytical EOS models, directly employing SESAME via Spiner, or directly using SESAME via EOSPAC6 (not optimized yet). Assuming Singularity moves forward as a common platform for the implementation of materials models, a decision will need to be made on which EOS interpolation package XCAP should move forward with, given resources and people are finite. We will attempt to address pros and cons of Spiner and EOSPAC6 and the trade-offs that should be considered during the decision making process. This report is intended as an ASC-PEM-EOS perspective on what is needed in an EOS interpolation package. Performance and Accuracy sections will mostly address data from comparison studies in LA-UR-22-22699.

In this work, we measure continuous thermal radiance from evolving clouds of liquid metal fragments ejected into vacuum, nonreactive, and reactive gas. We implement a model for the thermalization of the ejecta and gas and use this to constrain the absolute temperature of the ejecta cloud. This model enables further analyses of ejecta thermal behavior under a variety of conditions.

This manuscript investigates reactive- versus hydrodynamic-breakup processes of ejecta. For this study, the reactive metal is cerium (Ce) and the nonreactive metal is tin (Sn), the nonreactive gas is helium (He) and the reactive gas is deuterium (D2) or hydrogen (H2). Experiments were performed in vacuum and the reactive- and nonreactive-gases at various pressures, where we endeavored to match the post-shock gas densities to differentiate between reactive- versus hydrodynamic-breakup processes. Hydrodynamic breakup sensitively links to the Weber number (gas density, liquid fragment diameter, surface tension, and the square of the relative velocity between the fragment and the gas), whereas reactive breakup links to the reactive dynamics which includes two processes. In one case the reactive metal breaks up into smaller fragments as rapidly as the reaction rate, and in the other a crust grows on the liquid fragments as the reactions occur, a diffusion limited process. In the latter case, the particle diameters increase with time as the crust grows. In this process, which is indicated by the data, particles breakup as the CeD2 loses strength with increasing temperature, leaving an exponentially increasing diameter.

OpenSesame is a program for generating tabular equations of state (EOS), with capabilities for multiphase EOS construction. In this tutorial, we provide an overview of how to run OpenSesame to construct a multiphase EOS. We discuss some general features of OpenSesame, followed by a description of sample input files required for multiphase EOS construction. We also discuss how to extract data from EOS tables in order to compare to experimental data, with an example using the OpenSesame GUI. Lastly, we provide a description of how to generate ASCII-formatted EOS tables most often used by hydro code users.

We perform density functional theory (DFT) calculations of five solid phases and the liquid phase of tin. The calculations include cold curves of the five solid phases, phonon calculations in the quasiharmonic approximation over a range of volumes for each solid phase, and DFT-based molecular dynamics (DFT-MD) simulations of the liquid phase, including those of the melt curve using the Z method. Using the DFT results, we construct a tabular multiphase SESAME equation of state for tin, referred to as SESAME 2162. Comparisons to experimental data are made and show a high level of agreement in isobaric data, isothermal data, shock data, and phase boundary measurements, including measurements of the melt curve. The 2162 EOS will be useful for hydrodynamics simulations and has been designed with an eye toward hydrodynamics simulations that incorporate materials strength models and allow for modeling of the kinetics of phase transitions.

We report recent results of reactive and nonreactive metal fragments-ejecta-transporting in vacuum, and reactive and nonreactive gases. We postulate that reactive ejecta transporting in a reactive gas, such as D-2, will rapidly break up into smaller fragments in situations where they are otherwise hydrodynamically stable in a nonreactive gas such as He. The ejecta were formed through explosive loading of thin Sn (nonreactive) and Ce (reactive) coupons that included machined periodic perturbations on their backsides, which interfaced with vacuum, He or D-2. Coupon surface hydrodynamics, ejecta mass- and size-velocity distributions, and ejecta temperatures were diagnosed with laser doppler velocimetry, piezoelectric transducers, Mie scattering and infrared imaging (IR). In addition, particle imaging velocimetry was applied for the first time to evaluate ejecta transport to study ejecta sheet breakup dynamics. The IR data demonstrate that rapid reactions of Ce ejecta transporting in D-2 occur.

Shocked Ce metal in contact with a reactive gas such as H-2 or D-2 produces a distribution of ejecta particles that react with the gas to form Ce hydrides or deuterides. We present an average particle reaction diffusion model to calculate particle and gas temperatures and reaction fractions. We compare model results with recent HE driven Ce experiments into reactive D-2 and non-reactive He gases for a variety of initial gas pressures from 2-8 atmospheres at initial temperatures of 300 K. We find consistent agreement with radiance temperature measurements as a function of time using particle distributions from Mie scattering data resulting in Ce deuteride mass conversion fractions in D-2 gas of order 10 - 20 %.

This is a short, written addendum to the talk given on the progress and status of the phase aware multiphase project LA-UR 09-30168. The equation of state (EOS) project is working toward treating the material representation of phases, solids and liquids, as separate tables in an effort have more control of the physical material representations as required data for hydrocodes.

condensed matter system Hamiltonian. In addition to providing an introduction to the theoretical basis of the three-component model and an account of the empirical data utilized to construct an EOS, the aim of this paper is to enable readers to evaluate the applicability of a particular EOS within the context of a problem they are solving by reviewing the thermodynamic phase space in which it has been appropriately constrained. This paper does not aim to serve as an exhaustive documentation of the various methods used in construction of the SESAME tables. Instead, it focuses on the models used during the construction of a particular EOS for aluminum performed by Sjostrom et al. [SCR16] as an illustrative example.

A common paradigm used in the construction of equations of state is to decompose the thermodynamics into a superposition of three terms: a static-lattice cold curve, a contribution from the thermal motion of the nuclei, and a contribution from the thermal excitation of the electrons. While statistical mechanical models for crystals provide tractable framework for the nuclear contribution in the solid phase, much less is understood about the nuclear contribution above the melt temperature (C-v((nuc))approximate to 3)and how it should transition to the high-temperature limit (C-v((nuc))similar to 3/2R).In this work, we describe an algorithm for extracting both the thermal nuclear and thermal electronic contributions from quantum molecular dynamics (QMD) simulations. We then use the VASP QMD package to probe thermal nuclear behavior of liquid aluminum at normal density to compare the results to semi-empirical models - the Johnson generic model, the Chisolm hightemperature liquid model, and the CRIS model. The thermal electronic energy is also calculated from the VASP results and compared to the Kohn-Sham calculations from QE-DFT simulations, Green's function average atom calculations, and the Thomas-Fermi atomic model.

An extended Lagrangian framework for excited state molecular dynamics (XL-ESMD) using time-dependent self-consistent field theory is proposed. The formulation is a generalization of the extended Lagrangian formulations for ground state Born-Oppenheimer molecular dynamics [Phys. Rev. Lett. 2008 100, 123004]. The theory is implemented, demonstrated, and evaluated using a time-dependent semi empirical model, though it should be generally applicable to ab initio theory. The simulations show enhanced energy stability and a significantly reduced computational cost associated with the iterative solutions of both the ground state and the electronically excited states. Relaxed convergence criteria can therefore be used both for the self-consistent ground state optimization and for the iterative subspace diagonalization of the random phase approximation matrix used to calculate the excited state transitions. The XL-ESMD approach is expected to enable numerically efficient excited state molecular dynamics for such methods as time-dependent Hartree-Fock (TD-HF), Configuration Interactions Singles (CIS), and time-dependent density functional theory (TD-DFT).

We present a density functional theory study of cerium deuterides, varying deuterium content and temperature. Results are discussed in relation to ejecta experiments recently described in [J. Dynam. Mat. Behav. 1, 12 (2017)]. Using quantum molecular dynamics, we calculate diffusion coefficients, radial distribution functions, and heat capacities of these materials. Properties are calculated over temperatures ranging from 500-4000K at near ambient pressure and at 2.37 fold compression. We find that deuterium diffusion occurs rapidly accross this temperature and compression region and that heat capacity calculations are in agreement with approximations made in experiments. For cerium metal, a comparison of self-diffusion coefficient and viscosity with experimental data and analytical models shows excellent agreement. Further, we discuss the stucture of cerium deuterides with respect to radial distribution functions and provide fitted equations for diffusion coefficients over temperature.