Vertex degree distribution and arc endpoints degree distribution of graphs with a linear rule of preferential attachment and Pennock graphs

The article deals with two classes of growing random graphs following the preferential attachment rule with a linear weight function, L-graphs, and hybrid Pennock graphs. We determine the exact final vertex degree distribution and the exact final two-dimensional arcs degree distributions of graphs under consideration. The study proves that each hybrid Pennock graph is isomorphic to a certain L graph and that the converse does not hold since there are no Pennock graphs isomorphic to L graphs with negative displacements in the expression for the linear weight function. A formula is derived that makes it possible to determine the weight functions, which are used to generate graphs with the required asymptotic power-law vertex degree distribution. The reliability of the obtained results is confirmed by calculations using accurate numerical methods and simulation modeling, i.e. by direct generating of the graphs. The practical value of the results is demonstrated by an example of their effective application for accurate calibration of a growing graph that simulates a network of Internet at the level of autonomous systems.Comment: 12 pages, 8 figures, the article is prepared for the conference "Mechanical Science and Technology Update" (MSTU-2019

Role of the rho meson in the description of pion electroproduction experiments at JLab

We study the p(e,e' pi+)n reaction in the framework of an effective Lagrangian approach including nucleon, pi and rho meson degrees of freedom and show the importance of the rho-meson t-pole contribution to sigmaT, the transverse part of cross section. We test two different field representations of the rho meson, vector and tensor, and find that the tensor representation of the rho meson is more reliable in the description of the existing data. In particular, we show that the rho-meson t-pole contribution, including the interference with an effective non-local contact term, sufficiently improves the description of the recent JLab data at invariant mass W less 2.2 GeV and Q2 less 2.5 GeV2/c2. A ``soft'' variant of the strong piNN and rhoNN form factors is also found to be compatible with these data. On the basis of the successful description of both the sigmaL and sigmaT parts of the cross section we discuss the importance of taking into account the sigmaT data when extracting the charge pion form factor Fpi from sigmaL.Comment: 23 pages, 6 figures, accepted for publication in Phys. Rev.

Breit - Wigner parameters of nucleon resonance S11(1535)

The result of partial - wave analysis of angular distributions for the process gamma+p -> eta +p at the energies upto 2 GeV are given. From the energy dependence of the regression coefficient a0(W) the reliable estimates of Breit - Wigner parameters of S11(1535) - resonance and energy dependence of real and imagenery parts of electric dipol amplitude E0+ and its phase were obtainedComment: 12 pages, 11 figure

A generalized Ramsey excitation scheme with suppressed light shift

We experimentally investigate a recently proposed optical excitation scheme [V.I. Yudin et al., Phys. Rev. A 82, 011804(R)(2010)] that is a generalization of Ramsey's method of separated oscillatory fields and consists of a sequence of three excitation pulses. The pulse sequence is tailored to produce a resonance signal which is immune to the light shift and other shifts of the transition frequency that are correlated with the interaction with the probe field. We investigate the scheme using a single trapped 171Yb+ ion and excite the highly forbidden 2S1/2-2F7/2 electric-octupole transition under conditions where the light shift is much larger than the excitation linewidth, which is in the Hertz range. The experiments demonstrate a suppression of the light shift by four orders of magnitude and an immunity against its fluctuations.Comment: 5 pages, 4 figure

Polystyrene-based nanocomposites with different fillers: fabrication and mechanical properties

The paper presents a comprehensive analysis of elastic properties of polystyrene-based nanocomposites filled with different types of inclusions: small spherical particles (SiO2 and Al2O3), alumosilicates (montmorillonite, halloysite natural tubules and Mica) and carbon nanofillers (carbon black and multi-walled carbon nanotubes). Composites were fabricated by melt technology. The analysis of composite melts showed that the introduction of Montmorillonite, Multi-walled carbon nanotubes, and Al2O3 particles provided an increase in melt viscosity by an average of 2 to 5 orders of magnitude over the pure polystyrene. Block samples of composites with different filler concentrations were prepared, and their linear and nonlinear elastic properties were studied. The introduction of more rigid particles led to a more profound increase in the elastic modulus of the composite, with the highest rise of about 80% obtained with carbon fillers. Carbon black particles provided also an enhanced strength at break of about 20% higher than that of pure polystyrene. The nonlinear elastic moduli of composites were shown to be more sensitive to addition of filler particles to the polymer matrix than the linear ones. The nonlinearity coefficient $\beta$ comprising the combination of linear and nonlinear elastic moduli of a material demonstrated considerable changes correlating with changes of the Young's modulus. The absolute value of $\beta$ showed rise in 1.5-1.6 times in the CB- and HNT-containing composites as compared to that of pure PS. The changes in nonlinear elasticity of fabricated composites were compared with measurements of the parameters of bulk nonlinear strain waves in them. Variations of wave velocity and decay decrement correlated with observed enhancement of materials nonlinearity

Measurements of vector magnetic field using multiple electromagnetically induced transparency resonances in Rb vapor

We study intensity distribution of transmission resonances under the conditions of electromagnetically induced transparency (EIT) with lin||lin configuration in 87Rb vapor. We demonstrate that for various orientations of the external magnetic field all seven resolved EIT resonances exhibit maxima or minima at certain directions of the linear polarization of the laser field. This effect can be used for development of a high-precision vector EIT magnetometer.Comment: 4 pages, 4 figure