On an Optimal Interval Selection for the Regression of Molecular Frequency vs. Density Data Aimed at Determining Nonlinearity Parameters of Organic Liquids
Determining the isothermal and adiabatic nonlinearity parameters of liquids and soft matter is crucially important for a variety of engineering applications requiring operations under high pressures, nondestructive testing, exploring the propagation of finite amplitude and shock waves, etc. It has b...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-05-01
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| Series: | Computer Sciences & Mathematics Forum |
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| Online Access: | https://www.mdpi.com/2813-0324/7/1/25 |
| _version_ | 1797381438393286656 |
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| author | Roman N. Belenkov Eugene B. Postnikov |
| author_facet | Roman N. Belenkov Eugene B. Postnikov |
| author_sort | Roman N. Belenkov |
| collection | DOAJ |
| description | Determining the isothermal and adiabatic nonlinearity parameters of liquids and soft matter is crucially important for a variety of engineering applications requiring operations under high pressures, nondestructive testing, exploring the propagation of finite amplitude and shock waves, etc. It has been shown recently that mathematically this problem can be reduced to the initial value problem for an ODE build based on the linear response theory for thermodynamic equalities. The required initial conditions should be determined from thermodynamic measurements at ambient pressure (or along the saturation curve). From the physical point of view, the required regression leading to the determining nonlinearity parameters originates from certain regularities in the response of molecular oscillations to the density changes. In this work, we explore how this regression procedure should be optimized computationally with respect to temperature ranges, which exclude anomalies affecting parameters of equations used for the required predictive calculations under high pressures. The validity of the proposed approach is tested by case studies of the propagation of weakly non-linear waves with finite amplitudes and density changes due to shock waves under the Rankine–Hugoniot jump conditions. |
| first_indexed | 2024-03-08T20:52:30Z |
| format | Article |
| id | doaj.art-2daed19d40244ac59b6e2363cec5973f |
| institution | Directory Open Access Journal |
| issn | 2813-0324 |
| language | English |
| last_indexed | 2024-03-08T20:52:30Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Computer Sciences & Mathematics Forum |
| spelling | doaj.art-2daed19d40244ac59b6e2363cec5973f2023-12-22T14:02:06ZengMDPI AGComputer Sciences & Mathematics Forum2813-03242023-05-01712510.3390/IOCMA2023-14549On an Optimal Interval Selection for the Regression of Molecular Frequency vs. Density Data Aimed at Determining Nonlinearity Parameters of Organic LiquidsRoman N. Belenkov0Eugene B. Postnikov1Theoretical Physics Department, Kursk State University, Radishcheva St. 33, 305000 Kursk, RussiaTheoretical Physics Department, Kursk State University, Radishcheva St. 33, 305000 Kursk, RussiaDetermining the isothermal and adiabatic nonlinearity parameters of liquids and soft matter is crucially important for a variety of engineering applications requiring operations under high pressures, nondestructive testing, exploring the propagation of finite amplitude and shock waves, etc. It has been shown recently that mathematically this problem can be reduced to the initial value problem for an ODE build based on the linear response theory for thermodynamic equalities. The required initial conditions should be determined from thermodynamic measurements at ambient pressure (or along the saturation curve). From the physical point of view, the required regression leading to the determining nonlinearity parameters originates from certain regularities in the response of molecular oscillations to the density changes. In this work, we explore how this regression procedure should be optimized computationally with respect to temperature ranges, which exclude anomalies affecting parameters of equations used for the required predictive calculations under high pressures. The validity of the proposed approach is tested by case studies of the propagation of weakly non-linear waves with finite amplitudes and density changes due to shock waves under the Rankine–Hugoniot jump conditions.https://www.mdpi.com/2813-0324/7/1/25nonlinearity parameterGrüneisen parameterphonon theoryinitial value problemregression |
| spellingShingle | Roman N. Belenkov Eugene B. Postnikov On an Optimal Interval Selection for the Regression of Molecular Frequency vs. Density Data Aimed at Determining Nonlinearity Parameters of Organic Liquids Computer Sciences & Mathematics Forum nonlinearity parameter Grüneisen parameter phonon theory initial value problem regression |
| title | On an Optimal Interval Selection for the Regression of Molecular Frequency vs. Density Data Aimed at Determining Nonlinearity Parameters of Organic Liquids |
| title_full | On an Optimal Interval Selection for the Regression of Molecular Frequency vs. Density Data Aimed at Determining Nonlinearity Parameters of Organic Liquids |
| title_fullStr | On an Optimal Interval Selection for the Regression of Molecular Frequency vs. Density Data Aimed at Determining Nonlinearity Parameters of Organic Liquids |
| title_full_unstemmed | On an Optimal Interval Selection for the Regression of Molecular Frequency vs. Density Data Aimed at Determining Nonlinearity Parameters of Organic Liquids |
| title_short | On an Optimal Interval Selection for the Regression of Molecular Frequency vs. Density Data Aimed at Determining Nonlinearity Parameters of Organic Liquids |
| title_sort | on an optimal interval selection for the regression of molecular frequency vs density data aimed at determining nonlinearity parameters of organic liquids |
| topic | nonlinearity parameter Grüneisen parameter phonon theory initial value problem regression |
| url | https://www.mdpi.com/2813-0324/7/1/25 |
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