Singlet linear equation for one-particle distribution function in statistical physics of surface phenomena in liquids

Yu. V. Agrafonov ; I. S. Petrushin ; D. V. Khalaimov

Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 213 (2022), pp. 3-9.

Résumé

In this work we suggest the algorithm to solve the linear Fredholm integral equation of the second kind for the one-particle distribution function of simple liquid near the hard surface. The core and the right part of the equation are guessed using Percus-Yevick approximation defined on finite interval for spatial macroscopic liquid. We suggest an approach to solve the equation analytically for each interval where function is defined.

Détail

Keywords: supercooled liquid, ideal glass, partial distribution function, replicas, chaotic phase transition of the first kind, Fredholm equation of the second kind.

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