Studies on van der pol coupled systems

Summary Two Van der Pol equations with linear coupling are considered. The equations correspond to the mechanical one mass system with two degrees of freedom and with two types of self excited vibration generation. One due to presence of Van der Pol damping terms and second one due to the coordinate force which causes instability of equilibrium position of abbreviated system. The stationary one and two frequency oscillations as well as regions of parameters for different types of solution are discussed. Two types of bifurcations and amplitude relations are analyzed.

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Sommario Si considerano due equazioni di Van der Pol con l'accoppiamento lineare. Le equazioni corrispondono al sistema meccanico di una massa con due gradi di libertà e con due tipi di generazione di vibrazioni autoeccitanti. Una dovuta alla presenza di termini smorzanti di tipo Van der Pol, l'altra dovuta alla coordinata forza che causa instabilità della posizione di equilibrio del sistema ridotto. Si discutono le due oscillazioni di frequenza stazionarie e le regioni dei parametri per i diversi tipi di soluzione. Si analizzano due tipi di biforcazione e di relazione di ampiezza.

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On study leave at Department of Mechanical Engineering, The University of Alberta, Edmonton, Canada. T6G 2G8.     

Low-energy gluon to the vacuum polarization of heavy quarks

We calculate a correction to the effective electromagnetic current at low energies, induced by a heavy-quark loop, and determine the analytic structure of the vacuum polarization function at small q ², for which an explicit expression is given to the O(α _s ³ ) order of perturbation theory. Implications to the high-precision analysis of experimental data on heavy-quark production in e ⁺ e ^? annihilation are discussed.     

Parametric x-ray radiation from 500-MeV electrons in a tungsten single crystal with a surface mosaicity less than 1.5′

The yield of parametric x-ray radiation from a tungsten single crystal irradiated with a E=500 MeV electron beam from the Tomsk Sirius synchrotron was studied experimentally in Bragg geometry. The tungsten sample was 1.7 mm thick and had a surface mosaicity less than 1.5′; it was oriented in such a way that the (111) face was at the Bragg angle of θ _B=45° with respect to the electron-beam direction. The x-ray photons were detected at the angle of 2θ _B=90° with respect to the electron beam. The angular distributions of parametric x rays are compared with those calculatedwith allowance for actual experimental conditions.     

A New Qualitative Prediction of the Parton Model for High-Energy Hadron Collisions

Inclusive single jet production in hadron collisions is considered. It is shown that the QCD parton model predicts a nonmonotonic dependence of the inclusive cross section on the fraction of the energy deposited in the jet registered, if it is normalized on the same cross section measured at another collision energy. Specifically, if the cross section is normalized by the one measured at a higher collision energy, it possesses a minimum which depends on jet rapidity. This prediction can be tested at the Fermilab Tevatron, at the CERN LHC, and at the Very Large Hadron Collider under discussion.     

Manipulations with diamond nanoparticles in SPM: the effect of electric field of the conductive probe tip

The role of the electric field during manipulations with diamond nanoparticles on a silicon substrate by a scanning probe microscope (SPM) tip is studied. It is found that the attractive force appearing in the contact between nanodiamond and an electrically charged tip is sufficient to detach and displace a chosen nanoparticle from initial to goal position under moderate mechanical stresses of the probe to nanoparticle. The problem of the control of the tip motion trajectory during manipulations is solved by visualizing the tip trace of the sample surface. The results obtained will be used for precision positioning of single-photon emitters based on luminescent nanodiamonds in microcavities.     

Renormalization group analysis of the τ-lepton decay within QCD

A technique to sum up the regular corrections appearing under the analytical continuation from the space like momentum region to the time like one is proposed. A perturbative part of the inclusive semileptonic decay width of the τ-lepton in analyzed in detail.     

Detection of parametric X-ray radiation from moderately relativistic protons in crystals

The spectral maxima of parametric x-ray radiation that are emitted by moderately relativistic protons interacting with various crystals have been detected. The spectral positions of these maxima depend on the crystal orientation angle and they are consistent with the theoretical values. The measurements were carried out with silicon and graphite crystals on the 5-GeV proton beam extracted from the Nuclotron at the Laboratory of High Energies, JINR.     

Decays τ → (η, η')<Emphasis Type="Italic">K</Emphasis>–ν<Subscript>τ</Subscript> in the extended Nambu–Jona-Lasinio model

The decays τ → (η, η')K–ν_τ are described in the framework of the extended Nambu–Jona-Lasinio model. Both full and differential widths of these decays are calculated. The vector and scalar channels are considered. In the vector channel, the subprocesses with the intermediate K*(892) and K*(1410) mesons play the main role. In the scalar channel, the subprocesses with the intermediate and K₀^*(800) and K₀^*(1430) mesons are taken into account. The scalar channel gives an insignificant contribution to the full width of the decay τ → ηK–ν_τ. The obtained results are in satisfactory agreement with the experimental data. The prediction for the width of the process τ → η′K–ν_τ is made.