New analytic running coupling in QCD: higher loop levels

The properties of the new analytic running coupling are investigated at the higher loop levels. The expression for this invariant charge, independent of the normalization point, is obtained by invoking the asymptotic freedom condition. It is shown that at any loop level the relevant $\beta$ function has the universal behaviors at small and large values of the invariant charge. Due to this feature the new analytic running coupling possesses the universal asymptotics both in the ultraviolet and infrared regions irrespective of the loop level. The consistency of the model considered with the general definition of the QCD invariant charge is shown.Comment: LaTeX 2.09, 12 pages with 5 EPS figures, uses mpla1.sty; enlarged version is accepted for publication in Mod. Phys. Lett.

Analytic invariant charge and the lattice static quark-antiquark potential

A recently developed model for the QCD analytic invariant charge is compared with quenched lattice simulation data on the static quark-antiquark potential. By employing this strong running coupling one is able to obtain the confining quark-antiquark potential in the framework of the one-gluon exchange model. To achieve this objective a technique for evaluating the integrals of a required form is developed. Special attention is paid here to removing the divergences encountered the calculations. All this enables one to examine the asymptotic behavior of the potential at both small and large distances with high accuracy. An explicit expression for the quark-antiquark potential, which interpolates between these asymptotics, and satisfies the concavity condition, is proposed. The derived potential coincides with the perturbative results at small distances, and it is in a good agreement with the lattice data in the nonperturbative physically-relevant region. An estimation of the parameter $\Lambda_{QCD}$ is obtained for the case of pure gluodynamics. It is found to be consistent with all the previous estimations of $\Lambda_{QCD}$ in the framework of approach in hand.Comment: LaTeX2e, 10 pages with 3 EPS figure

Витискування елементів проникнення в перехідній зоні під дифузійними шарами, що зростають

The kinetics of diffusion of interstitial elements on the example of diffusion saturation with boron and silicon iron- carbon matrix (- iron) was considered . The layers of intermetallic Fe - B - Si are formed and grow in diffusion saturation , and carbon is pushed deep into the matrix. Linear , parabolic and logarithmic laws of motion of the interface boundary between the intermetallic layers and  steel  matrix was considered and solved the problem of the diffusion redistribution of carbon in the transition zone. Found that in all these cases is due to pushing of carbon  its concentration are increased at the interphase boundary . In case: a) the linear moving  of the interphase boundary carbon concentration at the interphase boundary is proportional to the thickness of protective coatings; b) the parabolic moving  of the interphase boundary carbon concentration at the boundary remains constant; c) the logarithmic moving  of the interphase boundary carbon concentration at the interphase boundary decreases with time.  Розглянута кінетика дифузії элементів проникнення на приикладі дифузійного насичення бором та сіліцієм залізо-вуглецевої матриці ( -залізо). В процесі дифузійного насичення утворюються і ростуть шари інтерметалідів системи Fe-B-Si, а вуглець витискується углиб матриці. Розглянуті лінійний, параболічний та логарифмічний закони руху міжфазної границі між шарами інтерметалідів і сталевою матрицею та розв'язані задачі про дифузійний перерозподіл вуглецю в переходній зоні. Встановлено, що в усіх розглянутих випадках внаслідок виштовхування вуглецю відбувається підвищення його концентрації на рухомій міжфазній границі. У випадку: а)лінійного закону руху концентрація вуглецю на міжфазній границі  зростає пропорційно товщині нанесеного захисного покриття; б) параболічного закону руху концентрація  вуглецю на границі залишається сталою; в) логарифмічного закону руху концентрація вуглецю на міжфазній зменшується з часом

A thick shell Casimir effect

We consider the Casimir energy of a thick dielectric-diamagnetic shell under a uniform velocity light condition, as a function of the radii and the permeabilities. We show that there is a range of parameters in which the stress on the outer shell is inward, and a range where the stress on the outer shell is outward. We examine the possibility of obtaining an energetically stable configuration of a thick shell made of a material with a fixed volume

Finite-element simulation of multiaxial compaction of sponge titanium powder

In this study, based on numerical simulation of multiaxial compaction process, an attempt is made to establish a consistent relation of material porosity to shearing and normal stresses under various stress state conditions. The finite element model of the multiaxial compression process has made it possible to apply both radial and axial pressures independently of one another. Powdered titanium sponge is modeled using the modified Drucker-Prager Cap plasticity model. A mathematical model of porosity alteration depending on the range of the equivalent pressure stress and the von Mises equivalent stress has been obtained. A comparison between finite-element simulation and experimental research on the die compaction of titanium sponge has been made. © 2016 Author(s)

LC nanocomposites: induced optical singularities, managed nano/micro structure, and electrical conductivity

Microstructure, phase transitions, electrical conductivity, and optical and electrooptical properties of multiwalled carbon nanotubes (NTs), dispersed in the cholesteric liquid crystal (cholesteryl oleyl carbonate, COC), nematic 5CB and their mixtures, were studied in the temperature range between 255 K and 363 K. The relative concentration X=COC/(COC+5CB)was varied within 0.0-1.0. The concentration $C_p$ of NTs was varied within 0.01-5% wt. The value of X affected agglomeration and stability of NTs inside COC+5CB. High-quality dispersion, exfoliation, and stabilization of the NTs were observed in COC solvent ("good" solvent). From the other side, the aggregation of NTs was very pronounced in nematic 5CB solvent ("bad" solvent). The dispersing quality of solvent influenced the percolation concentration $C_p$, corresponding to transition between the low conductive and high conductive states: e.g., percolation was observed at $C_p=1$ and $C_p=0.1$ for pure COC and 5CB, respectively. The effects of thermal pre-history on the heating-cooling hysteretic behavior of electrical conductivity were studied. The mechanism of dispersion of NTs in COC+5CB mixtures is discussed. Utilization of the mixtures of "good" and "bad" solvents allowed fine regulation of the dispersion, stability and electrical conductivity of LC+NTs composites. The mixtures of COC and 5CB were found to be promising for application as functional media with controllable useful chiral and electrophysical properties.Comment: 10 pages, 9 figure

Extended analytic QCD model with perturbative QCD behavior at high momenta

In contrast to perturbative QCD, the analytic QCD models have running coupling whose analytic properties correctly mirror those of spacelike observables. The discontinuity (spectral) function of such running coupling is expected to agree with the perturbative case at large timelike momenta; however, at low timelike momenta it is not known. In the latter regime, we parametrize the unknown behavior of the spectral function as a sum of (two) delta functions; while the onset of the perturbative behavior of the spectral function is set to be 1.0-1.5 GeV. This is in close analogy with the "minimal hadronic ansatz" used in the literature for modeling spectral functions of correlators. For the running coupling itself, we impose the condition that it basically merges with the perturbative coupling at high spacelike momenta. In addition, we require that the well-measured nonstrange semihadronic (V+A) tau decay ratio value be reproduced by the model. We thus obtain a QCD framework which is basically indistinguishable from perturbative QCD at high momenta (Q > 1 GeV), and at low momenta it respects the basic analyticity properties of spacelike observables as dictated by the general principles of the local quantum field theories.Comment: 15 pages, 6 figures; in v2 Sec.IV is extended after Eq.(48) and refs.[51-52] added; v2 published in Phys.Rev.D85,114043(2012

Analytic Invariant Charge in QCD

This paper gives an overview of recently developed model for the QCD analytic invariant charge. Its underlying idea is to bring the analyticity condition, which follows from the general principles of local Quantum Field Theory, in perturbative approach to renormalization group (RG) method. The concrete realization of the latter consists in explicit imposition of analyticity requirement on the perturbative expansion of $\beta$ function for the strong running coupling, with subsequent solution of the corresponding RG equation. In turn, this allows one to avoid the known difficulties originated in perturbative approximation of the RG functions. Ultimately, the proposed approach results in qualitatively new properties of the QCD invariant charge. The latter enables one to describe a wide range of the strong interaction processes both of perturbative and intrinsically nonperturbative nature.Comment: Invited review article; 46 pages, 14 EPS figure

Shock Wave Structure in a Strongly Nonlinear Granular Lattice with Viscous Dissipation

The shock wave structure in a one-dimensional lattice (e.g. granular chain) with a power law dependence of force on displacement between particles with viscous dissipation is considered and compared to the corresponding long wave approximation. A dissipative term depending on the relative velocity between neighboring particles is included in the discrete model to investigate its influence on the shape of steady shock profiles. The critical viscosity coefficient is obtained from the long-wave approximation for arbitrary values of the exponent n and denotes the transition from an oscillatory to a monotonic shock profile in stronly nonlinear systems. The expression for the critical viscosity coefficient converges to the known equation for the critical viscosity in the weakly nonlinear case. Values of viscosity based on this expression are comparable to the values obtained in the numerical analysis of a discrete particle lattice with a Herzian contact interaction corresponding to n = 3/2. An initial disturbance in a discrete system approaches a stationary shock profile after traveling a short distance that is comparable to the width of the leading pulse of a stationary shock front. The shock front width is minimized when the viscosity is equal to its critical value.Comment: 20 pages, 6 figure