On evaluation of two-loop self-energy diagram with three propogator

Small momentum expansion of the "sunset" diagram with three different masses is obtained. Coefficients at powers of $p^2$ are evaluated explicitly in terms of dilogarithms and elementary functions. Also some power expansions of "sunset" diagram in terms of different sets of variables are given.Comment: 9 pages, LaTEX, MSU-PHYS-HEP-Lu3/9

Gauge-Invariant Differential Renormalization: Abelian Case

A new version of differential renormalization is presented. It is based on pulling out certain differential operators and introducing a logarithmic dependence into diagrams. It can be defined either in coordinate or momentum space, the latter being more flexible for treating tadpoles and diagrams where insertion of counterterms generates tadpoles. Within this version, gauge invariance is automatically preserved to all orders in Abelian case. Since differential renormalization is a strictly four-dimensional renormalization scheme it looks preferable for application in each situation when dimensional renormalization meets difficulties, especially, in theories with chiral and super symmetries. The calculation of the ABJ triangle anomaly is given as an example to demonstrate simplicity of calculations within the presented version of differential renormalization.Comment: 15 pages, late

Ultrasound velocity measurements in high-chromium steel under plastic deformation

In the present study, the variation of the propagation velocity of ultrasound in the plastic deformation of corrosion-resistant high-chromium steel 40X13 with ferrite-carbide (delivery status), martensitic (quenched) and sorbitol (after high-temperature tempering) structures have beem studied/ It is found that each state shows its view of the loading curve. In the delivery state diagram loading is substantially parabolic throughout, while in the martensitic state contains only linear strain hardening step and in the sorbitol state the plastic flow curve is three-step. The velocity of ultrasonic surface waves (Rayleigh waves) was measured simultaneously with the registration of the loading curve in the investigated steel in tension. It is shown that the dependence of the velocity of ultrasound in active loading is determined by the law of plastic flow, that is, the staging of the corresponding diagram of loading. Structural state of the investigated steel is not only changing the type of the deformation curve under uniaxial tension, but also changes the nature of ultrasound speed of deformation

Research of the plastic flow of electrolytically saturated with hydrogen (He) Al-Cu-Mg alloy

The effect of hydrogen embrittlement on the plastic flow of Al-Cu-Mg alloy was investigated (HE). The studies were performed for the test samples of aluminum alloy subjected to electrolytic hydrogenation in a three electrode electrochemical cell. It is found that the mechanical properties and plastic flow curves of aluminum alloy are affected adversely by HE. These are found to show all the plastic flow stages: the linear, parabolic and pre-failure stages. It is established that the hydrogenation enhances the localization of straining leads to significant changes in the characteristics distances between local straining zones. The patterns of localized plasticity appear to be useful for a detailed analysis of plasticity exhibited by aluminum alloys

Effect of hydrogen on plastic strain localization and fracture of steels

The effect of interstitial hydrogen atoms on the mechanical properties and plastic strain localization patterns in tensile tested specimens of low-carbon steels have been studied using a double exposure speckle photography technique. It is found that the mechanical properties of low-carbon steels are affected adversely by hydrogen embrittlement. The deformation diagrams were examined for the deformed samples of low-carbon steels. These are found to show all the plastic flow stages: the linear, parabolic and pre-failure stages would occur for the respective values of the exponent n from the Ludwik-Holomon equation

High-precision molecular dynamics simulation of UO2-PuO2: superionic transition in uranium dioxide

Our series of articles is devoted to high-precision molecular dynamics simulation of mixed actinide-oxide (MOX) fuel in the rigid ions approximation using high-performance graphics processors (GPU). In this article we assess the 10 most relevant interatomic sets of pair potential (SPP) by reproduction of the Bredig superionic phase transition (anion sublattice premelting) in uranium dioxide. The measurements carried out in a wide temperature range from 300K up to melting point with 1K accuracy allowed reliable detection of this phase transition with each SPP. The {\lambda}-peaks obtained are smoother and wider than it was assumed previously. In addition, for the first time a pressure dependence of the {\lambda}-peak characteristics was measured, in a range from -5 GPa to 5 GPa its amplitudes had parabolic plot and temperatures had linear (that is similar to the Clausius-Clapeyron equation for melting temperature).Comment: 7 pages, 6 figures, 1 tabl

The Effect of Hydrogen on the Parameters of Plastic Deformation Localization in Low Carbon Steel

In the present study, the effect of interstitial hydrogen atoms on the mechanical properties and plastic strain localization patterns in tensile tested polycrystals of low-carbon steel Fe-0.07%C has been studied using double exposure speckle photography technique. The main parameters of plastic flow localization at various stages of deformation hardening have been determined in polycrystals of steel electrolytically saturated with hydrogen in a three-electrode electrochemical cell at a controlled constant cathode potential. Also, the effect of hydrogen on changing of microstructure by using optical microscopy has been demonstrated