{"title":"Virial equation of state for a granular system","authors":"Subhanker Howlader, Prasenjit Das","doi":"10.1140/epje/s10189-024-00412-z","DOIUrl":null,"url":null,"abstract":"<p>The equation of state for an ideal gas is simple, which is <span>\\(P=nk_\\textrm{B}T\\)</span>. In the case of imperfect gases where mutual interactions among the constituents are important, pressure <i>P</i> can be expressed as the series expansion of density <i>n</i> with appropriate coefficients, known as virial coefficients <span>\\(B_m\\)</span>. In this paper, we have obtained the first four virial coefficients for a model interaction potential <span>\\(\\Phi (r)\\)</span> using multidimensional Monte-Carlo integration and importance sampling methods. Next, we perform molecular dynamics simulations with the same <span>\\(\\Phi (r)\\)</span> for a many-particle system to obtain <i>P</i> as a function of <i>T</i> and <i>n</i>. We compare our numerical data with the virial equation of state.</p><p>The plot of Mayer function <i>f</i>(<i>r</i>) as a function of radial distance <i>r</i> for <span>\\(\\Theta (r)\\)</span> for different inverse temperature <span>\\(\\beta \\)</span>.</p>","PeriodicalId":790,"journal":{"name":"The European Physical Journal E","volume":"47 3","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"The European Physical Journal E","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1140/epje/s10189-024-00412-z","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"CHEMISTRY, PHYSICAL","Score":null,"Total":0}
引用次数: 0
Abstract
The equation of state for an ideal gas is simple, which is \(P=nk_\textrm{B}T\). In the case of imperfect gases where mutual interactions among the constituents are important, pressure P can be expressed as the series expansion of density n with appropriate coefficients, known as virial coefficients \(B_m\). In this paper, we have obtained the first four virial coefficients for a model interaction potential \(\Phi (r)\) using multidimensional Monte-Carlo integration and importance sampling methods. Next, we perform molecular dynamics simulations with the same \(\Phi (r)\) for a many-particle system to obtain P as a function of T and n. We compare our numerical data with the virial equation of state.
The plot of Mayer function f(r) as a function of radial distance r for \(\Theta (r)\) for different inverse temperature \(\beta \).
理想气体的状态方程很简单，即 P = n k B T。在不完全气体中，各成分之间的相互作用非常重要，压力 P 可以用密度 n 的序列展开来表示，并加上适当的系数，即维拉系数 B m。在本文中，我们利用多维蒙特卡洛积分法和重要性采样法获得了模型相互作用势 Φ ( r ) 的前四个病毒系数。接下来，我们用相同的 Φ ( r ) 对多粒子系统进行分子动力学模拟，得到 P 与 T 和 n 的函数关系。
期刊介绍：
EPJ E publishes papers describing advances in the understanding of physical aspects of Soft, Liquid and Living Systems.
Soft matter is a generic term for a large group of condensed, often heterogeneous systems -- often also called complex fluids -- that display a large response to weak external perturbations and that possess properties governed by slow internal dynamics.
Flowing matter refers to all systems that can actually flow, from simple to multiphase liquids, from foams to granular matter.
Living matter concerns the new physics that emerges from novel insights into the properties and behaviours of living systems. Furthermore, it aims at developing new concepts and quantitative approaches for the study of biological phenomena. Approaches from soft matter physics and statistical physics play a key role in this research.
The journal includes reports of experimental, computational and theoretical studies and appeals to the broad interdisciplinary communities including physics, chemistry, biology, mathematics and materials science.
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