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van Westen T. Algebraic second virial coefficient of the Mie m - 6 intermolecular potential based on perturbation theory. J Chem Phys 2021; 154:234502. [PMID: 34241261 DOI: 10.1063/5.0050659] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We propose several simple algebraic approximations for the second virial coefficient of fluids whose molecules interact by a generic Mie m - 6 intermolecular pair potential. In line with a perturbation theory, the parametric equations are formulated as the sum of a contribution due to a reference part of the intermolecular potential and a perturbation. Thereby, the equations provide a convenient (low-density) starting point for developing equation-of-state models of fluids or for developing similar approximations for the virial coefficient of (polymeric-)chain fluids. The choice of Barker and Henderson [J. Chem. Phys. 47, 4714 (1967)] and Weeks, Chandler, and Andersen [Phys. Rev. Lett. 25, 149 (1970); J. Chem. Phys. 54, 5237 (1971); and Phys. Rev. A 4, 1597 (1971)] for the reference part of the potential is considered. Our analytic approximations correctly recover the virial coefficient of the inverse-power potential of exponent m in the high-temperature limit and provide accurate estimates of the temperatures for which the virial coefficient equals zero or takes on its maximum value. Our description of the reference contribution to the second virial coefficient follows from an exact mapping onto the second virial coefficient of hard spheres; we propose a simple algebraic equation for the corresponding effective diameter of the hard spheres, which correctly recovers the low- and high-temperature scaling and limits of the reference fluid's second virial coefficient.
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Affiliation(s)
- Thijs van Westen
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, D-70569 Stuttgart, Germany
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2
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Gokul N, Schultz AJ, Kofke DA. Properties of supercritical N
2
, O
2
, CO
2
, and NH
3
mixtures from the virial equation of state. AIChE J 2020. [DOI: 10.1002/aic.17072] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
Affiliation(s)
- Navneeth Gokul
- Department of Chemical and Biological Engineering University at Buffalo, The State University of New York Buffalo New York USA
| | - Andrew J. Schultz
- Department of Chemical and Biological Engineering University at Buffalo, The State University of New York Buffalo New York USA
| | - David A. Kofke
- Department of Chemical and Biological Engineering University at Buffalo, The State University of New York Buffalo New York USA
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3
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Weinstein SJ, Holland MS, Rogers KE, Barlow NS. Analytic solution of the SEIR epidemic model via asymptotic approximant. PHYSICA D. NONLINEAR PHENOMENA 2020; 411:132633. [PMID: 32834248 PMCID: PMC7316071 DOI: 10.1016/j.physd.2020.132633] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/16/2020] [Accepted: 06/19/2020] [Indexed: 05/14/2023]
Abstract
An analytic solution is obtained to the SEIR Epidemic Model. The solution is created by constructing a single second-order nonlinear differential equation in ln S and analytically continuing its divergent power series solution such that it matches the correct long-time exponential damping of the epidemic model. This is achieved through an asymptotic approximant (Barlow et al., 2017) in the form of a modified symmetric Padé approximant that incorporates this damping. The utility of the analytical form is demonstrated through its application to the COVID-19 pandemic.
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Affiliation(s)
- Steven J. Weinstein
- School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY 14623, USA
- Department of Chemical Engineering, Rochester Institute of Technology, Rochester, NY 14623, USA
| | - Morgan S. Holland
- School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY 14623, USA
| | - Kelly E. Rogers
- School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY 14623, USA
| | - Nathaniel S. Barlow
- School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY 14623, USA
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Barlow NS, Weinstein SJ. Accurate closed-form solution of the SIR epidemic model. PHYSICA D. NONLINEAR PHENOMENA 2020; 408:132540. [PMID: 32362697 PMCID: PMC7195136 DOI: 10.1016/j.physd.2020.132540] [Citation(s) in RCA: 35] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/20/2020] [Revised: 04/24/2020] [Accepted: 04/27/2020] [Indexed: 05/19/2023]
Abstract
An accurate closed-form solution is obtained to the SIR Epidemic Model through the use of Asymptotic Approximants (Barlow et al., 2017). The solution is created by analytically continuing the divergent power series solution such that it matches the long-time asymptotic behavior of the epidemic model. The utility of the analytical form is demonstrated through its application to the COVID-19 pandemic.
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Affiliation(s)
- Nathaniel S. Barlow
- School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY 14623, USA
- Corresponding author.
| | - Steven J. Weinstein
- School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY 14623, USA
- Department of Chemical Engineering, Rochester Institute of Technology, Rochester, NY 14623, USA
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5
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Wheatley RJ, Schultz AJ, Do H, Gokul N, Kofke DA. Cluster integrals and virial coefficients for realistic molecular models. Phys Rev E 2020; 101:051301. [PMID: 32575236 DOI: 10.1103/physreve.101.051301] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2019] [Accepted: 04/27/2020] [Indexed: 06/11/2023]
Abstract
We present a concise, general, and efficient procedure for calculating the cluster integrals that relate thermodynamic virial coefficients to molecular interactions. The approach encompasses nonpairwise intermolecular potentials generated from quantum chemistry or other sources; a simple extension permits efficient evaluation of temperature and other derivatives of the virial coefficients. We demonstrate with a polarizable model of water. We argue that cluster-integral methods are a potent yet underutilized instrument for the development and application of first-principles molecular models and methods.
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Affiliation(s)
- Richard J Wheatley
- School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - Andrew J Schultz
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200, USA
| | - Hainam Do
- Department of Chemical and Environmental Engineering, University of Nottingham Ningbo China, 199 Taikang East Road, Ningbo 315100, China
| | - Navneeth Gokul
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200, USA
| | - David A Kofke
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200, USA
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Elliott JR, Schultz AJ, Kofke DA. Combined temperature and density series for fluid-phase properties. II. Lennard-Jones spheres. J Chem Phys 2019; 151:204501. [DOI: 10.1063/1.5126281] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- J. Richard Elliott
- Chemical and Biomolecular Engineering Department, The University of Akron, Akron, Ohio 44325-3906, USA
| | - Andrew J. Schultz
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200, USA
| | - David A. Kofke
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200, USA
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7
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Bhagwat SS, Kane A, Ganju S, Vora PP. Simple correlation for critical isotherm of pure compounds. Chem Eng Sci 2018. [DOI: 10.1016/j.ces.2018.08.043] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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8
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Subramanian R, Schultz AJ, Kofke DA. Direct orientation sampling of diatomic molecules for path integral Monte Carlo calculation of fully quantum virial coefficients. J Chem Phys 2017. [DOI: 10.1063/1.4977597] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Ramachandran Subramanian
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200, USA
| | - Andrew J. Schultz
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200, USA
| | - David A. Kofke
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200, USA
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Do H, Feng C, Schultz AJ, Kofke DA, Wheatley RJ. Calculation of high-order virial coefficients for the square-well potential. Phys Rev E 2016; 94:013301. [PMID: 27575230 DOI: 10.1103/physreve.94.013301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2016] [Indexed: 06/06/2023]
Abstract
Accurate virial coefficients B_{N}(λ,ɛ) (where ɛ is the well depth) for the three-dimensional square-well and square-step potentials are calculated for orders N=5-9 and well widths λ=1.1-2.0 using a very fast recursive method. The efficiency of the algorithm is enhanced significantly by exploiting permutation symmetry and by storing integrands for reuse during the calculation. For N=9 the storage requirements become sufficiently large that a parallel algorithm is developed. The methodology is general and is applicable to other discrete potentials. The computed coefficients are precise even near the critical temperature, and thus open up possibilities for analysis of criticality of the system, which is currently not accessible by any other means.
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Affiliation(s)
- Hainam Do
- School of Chemistry, University of Nottingham, University Park, NG7 2RD, United Kingdom
| | - Chao Feng
- Department of Computer Science and Engineering, University at Buffalo, The State University of New York, Buffalo, NY 14260-4200, USA
| | - Andrew J Schultz
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, NY 14260-4200, USA
| | - David A Kofke
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, NY 14260-4200, USA
| | - Richard J Wheatley
- School of Chemistry, University of Nottingham, University Park, NG7 2RD, United Kingdom
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Elliott JR, Schultz AJ, Kofke DA. Combined temperature and density series for fluid-phase properties. I. Square-well spheres. J Chem Phys 2015; 143:114110. [DOI: 10.1063/1.4930268] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- J. Richard Elliott
- Chemical and Biomolecular Engineering Department, The University of Akron, Akron, Ohio 44325-3906, USA
| | - Andrew J. Schultz
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200, USA
| | - David A. Kofke
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200, USA
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