On a Żołądek theorem

We prove the existence of cubic systems of the form $$ \begin{gathered} \dot x = y[1 - 2r(5 + 3r^2 )x + \gamma \lambda ^2 x^2 ] + a_0 x + a_1 x^2 + a_2 xy + a_3 y^2 + a_4 x^3 + a_5 x^2 y + a_6 xy^2 , \hfill \\ \dot y = - x(1 - 8rx)(1 - 3r\gamma x) - 2x[2(1 - 3r^2 ) - r\gamma (7 - 15r^2 )x]y \hfill \\ - [r(11 + r^2 ) + \gamma (1 - 22r^2 - 3r^4 )x]y^2 \hfill \\ - 2r\gamma \delta y^3 + a_0 y + a_7 x^2 + a_8 xy + a_9 y^2 + a_{10} x^3 + a_{11} x^2 y, \hfill \\ \end{gathered} $$ where α = 3r ² + 17, γ = r ² + 3, δ = 1 ? r ², and λ = 3r ² + 1, that have at least eleven limit cycles in a neighborhood of the point O(0, 0).     

Nilpotent centers of cubic systems

We present an explicit form of cubic systems with a nilpotent singular point of the focus or center type at the origin. A method for finding the focus quantities of such systems is indicated. Sufficient conditions for the existence of a nilpotent center for cubic systems are given. Cubic systems reducible to the Li´enard system are studied in detail.     

Comparative study of electronic structure of new superconductors (Sr, Ca)Pd2As2 and related compound BaPd2As2

This paper presents the comparative study of LDA calculated electronic structure of new isostructural to iron based systems superconductors (Sr, Ca)Pd₂As₂ with T _c about 1 K and similar but structurally different system BaPd₂As₂. Despite chemical formula looks similar to iron superconductors and even main structural motif is the same—layers of Fe square lattices, electronic structure of (Sr, Ca)Pd₂As₂ and BaPd₂As₂ differs from Fe (As, Se)-HTSC completely. All these systems have essentially three dimensional Fermi surfaces in contrast to Fe (As, Se) materials. The Fermi level is crossed by low intensive tails of Pd-4d and As-4p states. However, (Sr, Ca)Pd₂As₂ and BaPd₂As₂ materials have rather well developed peaks of Pd-4d (x ² ? y ²) band. Thus, by doping of about 2 holes per unit cell one can increase density of states at the Fermi level by a factor about 2.5. Since experimentally these compounds were found to be simple BCS superconductors the hole doping may considerably increase T _c . LDA calculated total densities of states at the Fermi level for stoichiometric systems perfectly agree with experimental estimates signifying rather small role of electronic correlations.     

Multiple bands: A key to high-temperature superconductivity in iron arsenides?

In the framework of four-band model of superconductivity in iron arsenides proposed by Barzykin and Gor’kov we analyze the gap ratios on hole—like and electron—like Fermi—surface cylinders. It is shown that experimentally observed (ARPES) gap ratios can be obtained only within rather strict limits on the values of pairing coupling constants. The difference of T _c values in 1111 and 122 systems is reasonably explained by the relative values of partial densities of states. The multiple bands electronic structure of these systems leads to a significant enhancement of effective pairing coupling constant determining T _c , so that high enough T _c values can be achieved even for the case of rather small intraband and interband pairing interactions. The article is published in the original.     

Analyzing the deformation of a porous medium with account for the collapse of pores

The generalized rheological method is used to construct a mathematical model of small deformations of a porous media with open pores. Changes in the resistance of the material to external mechanical impact at the moment of collapse of the pores is described using the von Mises–Schleicher strength condition. The irreversible deformation is accounted for with the help of the classic versions of the von Mises–Tresca–Saint-Venant yield condition and the condition that simulates the plastic loss of stability of the porous skeleton. Within the framework of the constructed model, this paper describes the analysis of the propagation of plane longitudinal compression waves in a homogeneous medium accompanied with plastic strain of the skeleton and densification of the material. A parallel computational algorithm is developed for the study of the elastoplastic deformation of the porous medium under external dynamics loads. The algorithm and the program are tested by calculating the propagation of plane longitudinal compression shock waves and the extension of the cylindrical cavity in an infinite porous medium. The calculation results are compared with exact solutions, and it is shown that they are in good agreement.     

Analysis of rotational motion of material microstructure particles by equations of the Cosserat elasticity theory

Oscillatory processes in media with microstructure under the action of concentrated impulse and time-periodic perturbations are analyzed within the Cosserat elasticity theory. According to the results of computations, such media are characterized by a resonance frequency equal to the frequency of natural oscillations of particle rotational motion. This frequency is a phenomenological parameter of a material. It was established that the oscillatory rotation of particles changes for monotone rotational motion with increasing intensity of shear strains.     

Electronic structure of new LiFeAs high-T c superconductor

We present results of ab initio LDA calculations of electronic structure of “next generation” layered iron-pnictide high-T _c superconductor LiFeAs (T _c = 18 K). Obtained electronic structure of LiFeAs very similar to recently studied ReOFeAs (Re = La, Ce, Pr, Nd, Sm) and AFe₂As₂ (A = Ba, Sr) compounds. Namely close to the Fermi level its electronic properties are also determined mainly by Fe 3d-orbilats of FeAs₄ two-dimensional layers. Band dispersions of LiFeAs are very similar to the LaOFeAs and BaFe₂As₂ systems as well as the shape of the Fe-3d density of states and Fermi surface. The article is published in the original.     

Interaction between antimony atoms and micropores in silicon

The interaction between Sb atoms and micropores of a getter layer in silicon is studied. The getter layer was obtained via implantation of Sb⁺ ions into silicon and subsequent heat treatment processes. The antimony atoms located in the vicinity of micropores are captured by micropores during gettering annealing and lose its electrical activity. The activation energy of capture process to the pores for antimony is lower than that of antimony diffusion in silicon deformation fields around microvoids on the diffusion process.     

Superconductivity in the exactly solvable model of pseudogap state: The absence of self-averaging

The features of the superconducting state are studied in the simple exactly solvable model of the pseudogap state induced by fluctuations of the short-range “dielectric” order in the model of the Fermi surface with “hot” spots. The analysis is carried out for arbitrary short-range correlation lengths ξ_corr. It is shown that the superconducting gap averaged over such fluctuations differs from zero in a wide temperature range above the temperature T _c of the uniform superconducting transition in the entire sample, which is a consequence of non-self-averaging of the superconducting order parameter over the random fluctuation field. In the temperature range T>T _c, superconductivity apparently exists in individual regions (drops). These effects become weaker with decreasing correlation length ξ_corr; in particular, the range of existence for drops becomes narrower and vanishes as ξ_corr → 0, but for finite values of ξ_corr, complete self-averaging does not take place.