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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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2
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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
- Corresponding author.
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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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4
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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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Barlow NS, Schultz AJ, Weinstein SJ, Kofke DA. Communication: Analytic continuation of the virial series through the critical point using parametric approximants. J Chem Phys 2015; 143:071103. [PMID: 26298108 DOI: 10.1063/1.4929392] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The mathematical structure imposed by the thermodynamic critical point motivates an approximant that synthesizes two theoretically sound equations of state: the parametric and the virial. The former is constructed to describe the critical region, incorporating all scaling laws; the latter is an expansion about zero density, developed from molecular considerations. The approximant is shown to yield an equation of state capable of accurately describing properties over a large portion of the thermodynamic parameter space, far greater than that covered by each treatment alone.
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Affiliation(s)
- Nathaniel S Barlow
- School of Mathematical Sciences, Rochester Institute of Technology, Rochester, New York 14623, USA
| | - Andrew J Schultz
- Department of Chemical and Biological Engineering, University at Buffalo, State University of New York, Buffalo, New York 14260, USA
| | - Steven J Weinstein
- Department of Chemical Engineering, Rochester Institute of Technology, Rochester, New York 14623, USA
| | - David A Kofke
- Department of Chemical and Biological Engineering, University at Buffalo, State University of New York, Buffalo, New York 14260, USA
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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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Schultz AJ, Kofke DA, Harvey AH. Molecular-based virial coefficients of CO2-H2O mixtures. AIChE J 2015. [DOI: 10.1002/aic.14880] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Affiliation(s)
- Andrew J. Schultz
- Dept. of Chemical and Biological Engineering; University at Buffalo; The State University of New York; Buffalo NY 14260
| | - David A. Kofke
- Dept. of Chemical and Biological Engineering; University at Buffalo; The State University of New York; Buffalo NY 14260
| | - Allan H. Harvey
- Applied Chemicals and Materials Div.; National Institute of Standards and Technology; Boulder CO 80305
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