The SPT2 approach is based on the scaled particle theory and developed for the description of thermodynamic properties of hard sphere (HS) fluids in disordered porous media. Using this approach a porous medium is modelled as a quenched matrix of hard spheres (HS) or overlapping hard spheres (OHS). A hard sphere fluid immersed in a matrix can move in a void between matrix particles. A number of approximations were previously proposed within the SPT2 approach. Among these approximations, the SPT2b1 has been considered as the most successful and accurate one in a large range of fluid densities and for different matrix parameters. However, at high densities, it can lack accuracy, since it does not take into account that the maximum packing fraction of a HS fluid in a matrix is limited, not by the geometrical porosity of a matrix 0 and the probe particle porosity , but by another type of porosity * introduced in our previous studies. The porosity * is related to the maximal adsorption capacity of a matrix and it is lower than 0 and larger than . This can be crucial for a fluid in matrices of low porosities and at high fluid density, especially in the region near close-packing conditions. Therefore, the approximations SPT2b2 and SPT2b3 taking into account this feature were suggested, although they still needed a correction because of their poor accuracy. In the present study, we improved the versions of these approximations, named as SPT2b2 * and SPT2b3 * . We compare these different approximations with the results of computer simulations performed in the Monte Carlo grand-canonical ensemble. We test the SPT2 approach both for the one-and three-dimensional cases. We show that the SPT2b3 * provides a very good description of the chemical potential of a confined fluid, which is better than others. This extends the applicability of the SPT2 approach to the studies of very dense fluids confined in disordered matrices.

The modified Poisson-Boltzmann theory of the restricted primitive model double layer is revisited and recast
\nin a fresh, slightly broader perspective. Derivation of relevant equations follow the techniques utilized in the
\nearlier MPB4 and MPB5 formulations and clarifies the relationship between these. The MPB4, MPB5, and a
\nnew formulation of the theory are employed in an analysis of the structure and charge reversal phenomenon
\nin asymmetric 2:1/1:2 valence electrolytes. Furthermore, polarization induced surface charge amplification is
\nstudied in 3:1/1:3 systems. The results are compared to the corresponding Monte Carlo simulations. The theories are seen to predict the “exact” simulation data to varying degrees of accuracy ranging from qualitative to
\nalmost quantitative. The results from a new version of the theory are found to be of comparable accuracy as the
\nMPB5 results in many situations. However, in some cases involving low electrolyte concentrations, theoretical
\nartifacts in the form of un-physical “shoulders” in the singlet ionic distribution functions are observed.

We consider a 2-1 electrolyte in contact with a narrow nanotube, which only\nallows one-dimensional storage along the axis. The asymmetry does not allow an\na priori definition of the potential of zero charge; instead, the natural\nreference is the electrode potential at which both ions have the same\nelectrochemical potential; the value of the latter can serve as a measure of\nionophilicity. Near this potential, ionophobic tubes are filled with a dilute\ngas, ionophilic tubes are filled with a one-dimensional solid containing about\nthe same number of the divalent ions and the monovalent counterions, a\nstructure that is stabilized by a strong screening of the Coulomb interaction\nby an induced counter charge on the walls of the tube. The filling of the tube\nby the application of an electrode potential exhibits a complicated pattern of\ninteractions between the two kinds of ions.\n

The optical, elastic anisotropic and thermodynamic properties of TiN in the NaCl (B1) structure are analyzed in detail in the temperature range from 0 to 2000 K and the pressure range from 0 to 20 GPa. From the calculated dielectric constants, a first order isostructural phase transition between 29 and 30 GPa is found for TiN. The absorption spectra exhibit high values ranging from the far infrared region to the ultra-violet one. The anisotropy value of Young's modulus of TiN is smaller than that of c-BN at 0 GPa and the anisotropy of TiN clearly increases with an increase of pressure. The effects of pressure and temperature on the bulk modulus, Gr\"uneisen parameter, Gibbs free energy, and Debye temperature are significant. The Gr\"uneisen parameter of TiN is much larger than that of c-BN. At temperatures below 1000 K, TiN's heat capacity is much larger than that of c-BN.

We considered intersubband electron transitions in an array of one-dimensional chains of spherical quantum dots in the GaAs/Al$_{x}$Ga$_{1-x}$As semiconductor system. The absorption coefficient caused by these transitions was calculated depending on frequency and polarization of incident light and on Fermi level position, and temperature. We established the existence of two maxima of the absorption coefficient at the edges of the absorption band. It is shown that the absorption coefficient reaches its maximal value at the center of the region between the $s$-, $p$-like subbands and slightly varies with temperature. The change of the direction of the linearly polarized light wave incident on the chains from perpendicular to parallel leads to a sharp narrowing of the absorption band. It is obtained that the absorption bandwidth increases with the reduction of the quantum dot radius. We also analyzed the dependence of the absorption coefficient of GaAs/Al$_{x}$Ga$_{1-x}$As superlattice on concentration of aluminium in the matrix.

In this review paper, the theory of synaptic transmission (ST) was developed and discussed. We used the hypothesis of isomorphism between: (a) the cooperative behavior of mediators --- acetylcholine molecules (ACh) and cholinoreceptors in a synaptic cleft with binding into mediator-receptor (AChR) complexes, (b) the critical phenomena in confined binary liquid mixtures. The systems of two (or three) nonlinear differential equations were proposed to find the change of concentrations of ACh, AChR complexes, and ferment acetylcholinesterase. The main findings of our study: the linear size of the activation zone was evaluated; the process of postsynaptic membrane activation was described as a cooperative process; different approximations of ACh synchronous release were examined; stationary states and types of singular points were studied for the proposed models of ST; the nonlinear kinetic model with three order parameters demonstrated a strange-attractor behavior.

The electronic energy band spectra, as well as partial and total density of\nelectronic states of the crystal argyrodite Ag$_{8}$SnSe$_{6}$ have been\nevaluated within the projector augmented waves (PAW) approach by means of the\nABINIT code. The one-electron energies have been evaluated using two\nfunctionals for exchange-correlation energy. The first one is the generalized\ngradient approximation (GGA) approach. The second one is the hybrid functional\nPBE0 composed of the semilocal GGA part and Hartree-Fock exact exchange\nnon-local energy for strongly correlated $4d$ electrons of Ag atom. The second\napproach eliminates the Coulomb self-interaction of the Ag $4d$ electrons. This\nleads to a significant restructuring of the energy bands in the filled valence\npart and to an improved location of the Ag $4d$-states on the energy scale, and\nthe resulting value of the band gap is well compared with experiment. The\neffects of strong correlation on the electronic structure of the crystal\nargyrodite are considered here for the first time.\n

Nature of extrinsic and intrinsic self-trapping (ST) of charge carriers in cuprates have been studied theoretically. The binding energies and radii of the extrinsic and intrinsic large polarons and bipolarons in cuprates are calculated variationally using the continuum model and adiabatic approximation. We have shown that the extrinsic and intrinsic three-dimensional (3D) large bipolarons exist in underdoped cuprates at $\eta=\varepsilon_{\infty}/\varepsilon_0<0.127$ and $\eta<0.138$, respectively [where $\varepsilon_{\infty}$ ($\varepsilon_0$) is the optic (static) dielectric constant].

The spectral relations for the four-time fermionic Green's functions are derived in the most general case. The terms which correspond to the zero-frequency anomalies, known before only for the bosonic Green's functions, are separated and their connection with the second cumulants of the Boltzmann distribution function is elucidated. The high-frequency expansions of the four-time fermionic Green's functions are provided for different directions in the frequency space.

A novel experimental paradigm and a novel modelling approach are presented to investigate oscillatory human motor performance by means of a key concept from condensed matter physics, namely, thermodynamic state variables. To this end, in the novel experimental paradigm participants performed pendulum swinging movements at self-selected oscillation frequencies in contrast to earlier studies in which pacing signals were used. Moreover, in the novel modelling approach, a canonical-dissipative limit cycle oscillator model was used with a conservative part that accounts for nonharmonic oscillator components in contrast to earlier studies in which only harmonic components were considered. Consistent with the Landau theory of magnetic phase transitions, we found that the oscillator model free energy decayed when participants performed oscillations further and further away from the Hopf bifurcation point of the canonical-dissipative limit cycle oscillator.