### Article

## Competitive 0 and π states in S/F/S trilayers: Multimode approach

We investigate the behavior of the critical temperature T_c in superconductor/ferromagnet/superconductor (S/F/S) trilayers in the dirty limit as a function of the ferromagnetic layer thickness d_f and the S/F interface transparency. We perform T_c calculations using the general self-consistent multimode approach based on the Usadel equations in Matsubara Green’s functions technique, and compare the results with the singlemode approximation, widely used in literature. Both methods produce similar results for sufficiently low interface transparency. For transparent interfaces, we obtain a qualitatively different T_c(d_f) behavior. Using the multimode approach, we observe multiple 0-π transitions in critical temperature, which cannot be resolved by the single-mode approximation. We also calculate the critical S layer thickness at given d_f when an S/F/S trilayer still has a nonzero critical temperature. Finally, we establish the limits of applicability of the single-mode approximation.

Using the Usadel equation approach, we have calculated the critical current density in ferromagnetic (F) Josephson junctions of different types containing insulating (I) and normal metal (N) layers in the weak link region. Even a thin additional N layer may change the boundary conditions at the SF or IF interface, where S is a superconducting electrode. We show that inserting an N layer may increase the critical current density Jc and shift the 0- transition to larger or smaller values of the thickness dF of the ferromagnet, depending on the boundary parameters.

In this paper, we construct a new distribution corresponding to a real noble gas as well as the equation of state for it.

The thermodynamical potential of a superconducting quantum cylinder is calculated. The dependence of the critical temperature and the heat capacity of a superconducting system of the surface concentration of electrons and on the radius of the nanotube is studied.

For a gas mixture, the new concept of number-theoretic internal energy is introduced. This energy does not depend on the masses of the miscible gases.

The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.

Radiation conditions are described for various space regions, radiation-induced effects in spacecraft materials and equipment components are considered and information on theoretical, computational, and experimental methods for studying radiation effects are presented. The peculiarities of radiation effects on nanostructures and some problems related to modeling and radiation testing of such structures are considered.

The paper provides a number of proposed draft operational guidelines for technology measurement and includes a number of tentative technology definitions to be used for statistical purposes, principles for identification and classification of potentially growing technology areas, suggestions on the survey strategies and indicators. These are the key components of an internationally harmonized framework for collecting and interpreting technology data that would need to be further developed through a broader consultation process. A summary of definitions of technology already available in OECD manuals and the stocktaking results are provided in the Annex section.