Registration Number
0223U003113,
0120U102051
, R & D reports
Title
Complex studies of relationship between interaction parameters and macroscopic features of classic and quantum systems.
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Head
Ushcats Mykhailo V., Доктор фізико-математичних наук
Registration Date
30-03-2023
Organization
Admiral Makarov National University of Shipbuilding
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The research object is the behavior of classical and quantum systems with a large number of particles in various aggregate states depending on the parameters of the interparticle interaction potential and external factors; phase transitions in such systems. The aim is analytical and numerical studies of the relationship between the macroscopic physical properties of matter (classical and quantum fluids, solids, etc.) and the parameters of its microstructure (geometric structure at the micro level, nature of interparticle interaction, etc.). Research methods – method of structural units; the partition function cluster expansion for systems of interacting particles and the corresponding equations of state in terms of reducible and irreducible cluster integrals. Based on the method of structural units, mathematical models are developed for dynamic physical processes of deformation, heat transfer and thermal expansion in solids and corresponding numerical studies are performed on the basis of those models. A new approximation of reducible integrals is proposed on the basis of information on the values of phase transition activity and several first irreducible integrals. This approximation, for the first time, provides a possibility to reproduce with high accuracy: a) subcritical isotherms for model systems as well as real fluids from their dilute gaseous states up to the two-phase region beyond the saturation point; b) magnetization curves of various two-dimensional and three-dimensional models of ferromagnets; c) binodals of the order-disorder transitions for the corresponding models of antiferromagnets; d) phase-equilibrium diagrams for the lattice models of binary mixtures (solutions). It is also proved that the cluster expansion accurately describes the Bose–Einstein condensation in the system of ideal bosons, which, in turn, provides an opportunity of its future usage in theoretical description of more complex quantum systems.
Product Description
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Evfimko Kostyantyn D.
Artykulnyi Oleksandr Petrovich
Bulavin Leonid A.
Mochalov Olexander O.
Svechnikova Oksana S.
Ushcats Svitlana Yu.
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2023-03-30
