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Murillo MS, Marciante M, Stanton LG. Machine Learning Discovery of Computational Model Efficacy Boundaries. PHYSICAL REVIEW LETTERS 2020; 125:085503. [PMID: 32909767 DOI: 10.1103/physrevlett.125.085503] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/28/2019] [Accepted: 07/30/2020] [Indexed: 06/11/2023]
Abstract
Computational models are formulated in hierarchies of variable fidelity, often with no quantitative rule for defining the fidelity boundaries. We have constructed a dataset from a wide range of atomistic computational models to reveal the accuracy boundary between higher-fidelity models and a simple, lower-fidelity model. The symbolic decision boundary is discovered by optimizing a support vector machine on the data through iterative feature engineering. This data-driven approach reveals two important results: (i) a symbolic rule emerges that is independent of the algorithm, and (ii) the symbolic rule provides a deeper understanding of the fidelity boundary. Specifically, our dataset is composed of radial distribution functions from seven high-fidelity methods that cover wide ranges in the features (element, density, and temperature); high-fidelity results are compared with a simple pair-potential model to discover the nonlinear combination of the features, and the machine learning approach directly reveals the central role of atomic physics in determining accuracy.
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Affiliation(s)
- Michael S Murillo
- Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, Michigan 48824, USA
| | | | - Liam G Stanton
- Department of Mathematics and Statistics, San José State University, San José, California 95192, USA
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2
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Characterization of molecular-atomic transformation in fluid hydrogen under pressure via long-wavelength asymptote of charge density fluctuations. J Mol Liq 2020. [DOI: 10.1016/j.molliq.2020.113274] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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3
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Klevets I, Bryk T. Ab initio study of electron-ion structure factors in binary liquids with different types of chemical bonding. J Chem Phys 2014; 141:214504. [DOI: 10.1063/1.4902543] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Liberatore E, Pierleoni C, Ceperley DM. Liquid-solid transition in fully ionized hydrogen at ultra-high pressures. J Chem Phys 2011; 134:184505. [DOI: 10.1063/1.3586808] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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5
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Santamaria R, Soullard J, Jellinek J. Thermal behavior of a 13-molecule hydrogen cluster under pressure. J Chem Phys 2010; 132:124505. [DOI: 10.1063/1.3359460] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
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Chamel N, Haensel P. Physics of Neutron Star Crusts. LIVING REVIEWS IN RELATIVITY 2008; 11:10. [PMID: 28163609 PMCID: PMC5255077 DOI: 10.12942/lrr-2008-10] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 09/05/2008] [Indexed: 05/28/2023]
Abstract
The physics of neutron star crusts is vast, involving many different research fields, from nuclear and condensed matter physics to general relativity. This review summarizes the progress, which has been achieved over the last few years, in modeling neutron star crusts, both at the microscopic and macroscopic levels. The confrontation of these theoretical models with observations is also briefly discussed.
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Affiliation(s)
- Nicolas Chamel
- Institut d’Astronomie et d’Astrophysique, Université Libre de Bruxelles, CP226, Boulevard du Triomphe, B-1050 Brussels, Belgium
| | - Pawel Haensel
- Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, Bartycka 18, 00-716 Warszawa, Poland
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Jakob B, Reinhard PG, Toepffer C, Zwicknagel G. Wave packet simulation of dense hydrogen. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:036406. [PMID: 17930350 DOI: 10.1103/physreve.76.036406] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2007] [Revised: 05/31/2007] [Indexed: 05/25/2023]
Abstract
Dense hydrogen is studied in the framework of wave packet molecular dynamics. In this semiquantal many-body simulation method the electrons are represented by wave packets which are suitably parametrized. The equilibrium properties and time evolution of the system are obtained with the help of a variational principle. At room temperature the results for the isotherms are in good agreement with anvil experiments. At higher densities beyond the range of the experimental data a transition from a molecular to a metallic state is predicted. The wave packets become delocalized and the electrical conductivity increases sharply. The phase diagram is calculated in a wide range of the pressure-density-temperature space. The observed transition from the molecular to metallic state is accompanied by an increase in density in agreement with recent reverberating shock wave experiments.
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Affiliation(s)
- B Jakob
- Institut für Theoretische Physik II, Universität Erlangen-Nürnberg, Staudtstrasse 7, D-91058 Erlangen, Germany
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Mazevet S, Lambert F, Bottin F, Zérah G, Clérouin J. Ab initio molecular dynamics simulations of dense boron plasmas up to the semiclassical Thomas-Fermi regime. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:056404. [PMID: 17677179 DOI: 10.1103/physreve.75.056404] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/20/2006] [Indexed: 05/16/2023]
Abstract
We build an "all-electron" norm-conserving pseudopotential for boron which extends the use of ab initio molecular dynamics simulations up to 50 times the normal density rho0. This allows us to perform ab initio simulations of dense plasmas from the regime where quantum mechanical effects are important to the regime where semiclassical simulations based on the Thomas-Fermi approach are, by default, the only simulation method currently available. This study first allows one to establish, for the case of boron, the density regime from which the semiclassical Thomas-Fermi approach is legitimate and sufficient. It further brings forward various issues pertaining to the construction of pseudopotentials aimed at high-pressure studies.
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Affiliation(s)
- S Mazevet
- Département de Physique Théorique et Appliquée, CEA/DAM Ile-de-France, BP12, 91680 Bruyères-le-Châtel Cedex, France
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Sumi T, Sekino H. A crossover from metal to plasma in dense fluid hydrogen. J Chem Phys 2007; 125:194526. [PMID: 17129142 DOI: 10.1063/1.2390704] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Thermodynamic properties in dense fluid hydrogen are studied by using a density-functional theory for electron-proton binary mixtures that is called quantal hypernetted-chain (QHNC) integral equation. A nonlocal approximation for the exchange-correlation potential in a finite-temperature Kohn-Sham equation is presented. Results obtained from the QHNC with the nonlocal approximation are compared with those obtained from the QHNC with a local density approximation. Temperature variation of thermodynamic quantities between 10(4) and 10(6) K are investigated along an isochor specified by a dimensionless density parameter of rs=0.5. These quantities obtained from the QHNCs show that a crossover from metal to plasma occurs around a temperature of T=1.78 x 10(5) K. Electrical resistivity Re of the dense fluid hydrogen evaluated from a Ziman formula [The Properties of Liquid Metals, edited by S. Takenohi (Wiley, New York, 1973)] extended to finite temperature is about 0.7 muOmega cm at T=10(4) K. The dense fluid hydrogen at the temperature can be considered as a metallic fluid, because the value is smaller than typical values of Re in alkali metals at room temperature. The Re slightly increases with the temperature increase, and the temperature valuation of Re is monotonic. We clearly show that the contribution from the electronic excited states plays an important role for the sharp crossover from the metal to the plasma, and that the crossover is interpreted as a crossover from degenerate electron gas to nondegenerate electron gas.
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Affiliation(s)
- Tomonari Sumi
- Department of Knowledge-based Information Engineering, Toyohashi University of Technology, Toyohashi 441-8580, Japan.
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Delaney KT, Pierleoni C, Ceperley DM. Quantum Monte Carlo simulation of the high-pressure molecular-atomic crossover in fluid hydrogen. PHYSICAL REVIEW LETTERS 2006; 97:235702. [PMID: 17280214 DOI: 10.1103/physrevlett.97.235702] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2006] [Indexed: 05/13/2023]
Abstract
A first-order liquid-liquid phase transition in high-pressure hydrogen between molecular and atomic fluid phases has been predicted in computer simulations using ab initio molecular dynamics approaches. However, experiments indicate that molecular dissociation may occur through a continuous crossover rather than a first-order transition. Here we study the nature of molecular dissociation in fluid hydrogen using an alternative simulation technique in which electronic correlation is computed within quantum Monte Carlo methods, the so-called coupled electron-ion Monte Carlo method. We find no evidence for a first-order liquid-liquid phase transition.
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Affiliation(s)
- Kris T Delaney
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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Pierleoni C, Ceperley DM. Computational Methods in Coupled Electron-Ion Monte Carlo Simulations. Chemphyschem 2005; 6:1872-8. [PMID: 16088971 DOI: 10.1002/cphc.200400587] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
In the last few years, we have been developing a Monte Carlo simulation method to cope with systems of many electrons and ions in the Born-Oppenheimer approximation: the coupled electron-ion Monte Carlo method (CEIMC). Electronic properties in CEIMC are computed by quantum Monte Carlo rather than by density functional theory (DFT) based techniques. CEIMC can, in principle, overcome some of the limitations of the present DFT-based ab initio dynamical methods. The new method has recently been applied to high-pressure metallic hydrogen. Herein, we present a new sampling algorithm that we have developed in the framework of the reptation quantum Monte Carlo method chosen to sample the electronic degrees of freedom, thereby improving its efficiency. Moreover, we show herein that, at least for the case of metallic hydrogen, variational estimates of the electronic energies lead to an accurate sampling of the proton degrees of freedom.
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Affiliation(s)
- Carlo Pierleoni
- Department of Physics, University of L'Aquila, Via Vetoio, 67010 L'Aquila, Italy.
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Mazevet S, Desjarlais MP, Collins LA, Kress JD, Magee NH. Simulations of the optical properties of warm dense aluminum. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:016409. [PMID: 15697737 DOI: 10.1103/physreve.71.016409] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2004] [Indexed: 05/24/2023]
Abstract
Using quantum molecular dynamics simulations, we show that the optical properties of aluminum change drastically along the nonmetal metal transition observed experimentally. As the density increases and the many-body effects become important, the optical response gradually evolves from the one characteristic of an atomic fluid to the one of a simple metal. We show that quantum molecular dynamics combined with the Kubo-Greenwood formulation naturally embodies the two limits and provides a powerful tool to calculate and benchmark the optical properties of various systems as they evolve into the warm dense matter regime.
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Affiliation(s)
- S Mazevet
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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Pierleoni C, Ceperley DM, Holzmann M. Coupled electron-ion monte carlo calculations of dense metallic hydrogen. PHYSICAL REVIEW LETTERS 2004; 93:146402. [PMID: 15524818 DOI: 10.1103/physrevlett.93.146402] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2004] [Indexed: 05/24/2023]
Abstract
We present an efficient new Monte Carlo method which couples path integrals for finite temperature protons with quantum Monte Carlo calculations for ground state electrons, and we apply it to metallic hydrogen for pressures beyond molecular dissociation. We report data for the equation of state for temperatures across the melting of the proton crystal. Our data exhibit more structure and higher melting temperatures of the proton crystal than do Car-Parrinello molecular dynamics results. This method fills the gap between high temperature electron-proton path integral and ground state diffusion Monte Carlo methods and should have wide applicability.
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Affiliation(s)
- Carlo Pierleoni
- INFM and Department of Physics, Università of L' Aquila, Via Vetoio, I-67010 L'Aquila, Italy
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Matsuishi K, Gregoryanz E, Mao HK, Hemley RJ. Equation of state and intermolecular interactions in fluid hydrogen from Brillouin scattering at high pressures and temperatures. J Chem Phys 2003. [DOI: 10.1063/1.1575196] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Ceperley D, Dewing M, Pierleoni C. The Coupled Electronic-Ionic Monte Carlo Simulation Method. BRIDGING TIME SCALES: MOLECULAR SIMULATIONS FOR THE NEXT DECADE 2002. [DOI: 10.1007/3-540-45837-9_17] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
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Clérouin J, Dufrêche JF. Ab initio study of deuterium in the dissociating regime: sound speed and transport properties. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:066406. [PMID: 11736281 DOI: 10.1103/physreve.64.066406] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2001] [Indexed: 05/23/2023]
Abstract
The sound speed and the transport properties of dense hydrogen (deuterium) are computed from local spin-density approximation molecular-dynamics simulations in the dissociating regime. The sound speed c(s) is evaluated from the thermodynamical differentiation of the equation of state in the molecular phase and is in very good agreement with recent experiments. The diffusion constant D and the viscosity eta are extracted from simulations performed at V=6, 4, and 2.7 cm(3)/mole, corresponding, respectively, for deuterium at rho=0.672, 1.0, and 1.5 g/cm(3) in a range of temperatures 1000 K<T<50,000 K. In the dissociated regime, the diffusion coefficient is well predicted by one-component plasma formulas using a renormalized coupling parameter recently proposed by Murillo [M. S. Murillo, Phys. Rev. B 62, 4115 (2000)]. The behavior of the shear viscosity in the dissociated regime is more complex and exhibits a crossover between atomic and screened plasma formulation. A comparison with recent molecular-dynamics simulations of Yukawas systems shows that the inverse of the screening length must lie between 1 and 2, in nearest-neighbor radius units, as suggested by the results on the diffusion.
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Affiliation(s)
- J Clérouin
- Commissariat à l'Energie Atomique/DIF, Département de Physique Théorique et Appliquée, Boîte Postale 12, 91680 Bruyères le Châtel Cedex, France.
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