Geodesic
Singlet linear equation for one-particle distribution function in statistical physics of surface phenomena in liquids
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 213 (2022), pp. 3-9

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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.
Keywords: supercooled liquid, ideal glass, partial distribution function, replicas, chaotic phase transition of the first kind, Fredholm equation of the second kind. 
@article{INTO_2022_213_a0,
     author = {Yu. V. Agrafonov and I. S. Petrushin and D. V. Khalaimov},
     title = {Singlet linear equation for one-particle distribution function in statistical physics of surface phenomena in liquids},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {3--9},
     publisher = {mathdoc},
     volume = {213},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_213_a0/}
}
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Yu. V. Agrafonov; I. S. Petrushin; D. V. Khalaimov. Singlet linear equation for one-particle distribution function in statistical physics of surface phenomena in liquids. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 213 (2022), pp. 3-9. http://geodesic.mathdoc.fr/item/INTO_2022_213_a0/