Thermal conductivity in dynamics of first-order phase transition

Effects of thermal conductivity on the dynamics of first-order phase transitions are studied. Important consequences of a difference of the isothermal and adiabatic spinodal regions are discussed. We demonstrate that in hydrodynamical calculations at non-zero thermal conductivity, $\kappa \neq 0$, onset of the spinodal instability occurs, when the system trajectory crosses the isothermal spinodal line. Only for $\kappa = 0$ it occurs at a cross of the adiabatic spinodal line. Therefore ideal hydrodynamics is not suited for an appropriate description of first-order phase transitions.Comment: 21 pages, 2 figures; submitted to Nuclear Physics A on 26 Feb 201

Viscosity and thermal conductivity effects at first-order phase transitions in heavy-ion collisions

Effects of viscosity and thermal conductivity on the dynamics of first-order phase transitions are studied. The nuclear gas-liquid and hadron-quark transitions in heavy-ion collisions are considered. We demonstrate that at non-zero thermal conductivity, $\kappa \neq 0$, onset of spinodal instabilities occurs on an isothermal spinodal line, whereas for $\kappa =0$ instabilities take place at lower temperatures, on an adiabatic spinodal.Comment: invited talk at 6th International Workshop on Critical Point and Onset of Deconfinment (CPOD2010), Dubna, August 22-28, 201

Special elements of the lattice of epigroup varieties

We study special elements of eight types (namely, neutral, standard, costandard, distributive, codistributive, modular, lower-modular and upper-modular elements) in the lattice EPI of all epigroup varieties. Neutral, standard, costandard, distributive and lower-modular elements are completely determined. A strong necessary condition and a sufficient condition for modular elements are found. Modular elements are completely classified within the class of commutative varieties, while codistributive and upper-modular elements are completely determined within the wider class of strongly permutative varieties. It is verified that an element of EPI is costandard if and only if it is neutral; is standard if and only if it is distributive; is modular whenever it is lower-modular; is neutral if and only if it is lower-modular and upper-modular simultaneously. We found also an application of results concerning neutral and lower-modular elements of EPI for studying of definable sets of epigroup varieties.Comment: In comparison with the previous version, we slightly optimize the proof of Theorem 1.1, eliminate a few typos and add Question 11.

Cancellable elements of the lattices of varieties of semigroups and epigroups

We completely determine all semigroup [epigroup] varieties that are cancellable elements of the lattice of all semigroup [respectively epigroup] varieties.Comment: 17 pages, 3 figures. Compared with the previous version, we add Corollary 1.4 and Figure 1 and fix several typos. arXiv admin note: text overlap with arXiv:1806.0597